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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.11052">arXiv:2212.11052</a> <span> [<a href="https://arxiv.org/pdf/2212.11052">pdf</a>, <a href="https://arxiv.org/ps/2212.11052">ps</a>, <a href="https://arxiv.org/format/2212.11052">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Restriction theorem for Fourier-Dunkl transform II: Paraboloid, sphere, and hyperboloid surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Senapati%2C+P+J+K">P Jitendra Kumar Senapati</a>, <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Mondal%2C+S+S">Shyam Swarup Mondal</a>, <a href="/search/math?searchtype=author&query=Mejjaoli%2C+H">Hatem Mejjaoli</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.11052v1-abstract-short" style="display: inline;"> This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on $\mathbb{R}^{n}\times\mathbb{R}^{d}$. The main novelty of this paper is that we here prove Strichartz's restriction theorem for the Fourier-Dunkl transform for certain… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11052v1-abstract-full').style.display = 'inline'; document.getElementById('2212.11052v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.11052v1-abstract-full" style="display: none;"> This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on $\mathbb{R}^{n}\times\mathbb{R}^{d}$. The main novelty of this paper is that we here prove Strichartz's restriction theorem for the Fourier-Dunkl transform for certain surfaces, namely, paraboloid, sphere, and hyperboloid and its generalisation to the family of orthonormal functions. Finally, as an application of these restriction theorems, we establish versions of Strichartz estimates for orthonormal families of initial data associated with Schr枚dinger's propagator in the case of the Dunkl Laplacian and Klein-Gordon operator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11052v1-abstract-full').style.display = 'none'; document.getElementById('2212.11052v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 42A38; 47B10; Secondary: 42B35; 43A32 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.01886">arXiv:2212.01886</a> <span>  </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Restriction theorem for the Fourier-Dunkl transform I: Cone surface </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Senapati%2C+P+J+K">P Jitendra Kumar Senapati</a>, <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Mondal%2C+S+S">Shyam Swarup Mondal</a>, <a href="/search/math?searchtype=author&query=Mejjaoli%2C+H">Hatem Mejjaoli</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.01886v2-abstract-short" style="display: inline;"> In this article, we define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz's restriction theorem for the Fourier-Dunkl transform for a cone-hyper-surface and its generalisation to the family of orthonormal functions. As an application of this restriction theorem, we derive the Strichartz inequality associated with the square root of Dunkl Laplacian for the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.01886v2-abstract-full').style.display = 'inline'; document.getElementById('2212.01886v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.01886v2-abstract-full" style="display: none;"> In this article, we define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz's restriction theorem for the Fourier-Dunkl transform for a cone-hyper-surface and its generalisation to the family of orthonormal functions. As an application of this restriction theorem, we derive the Strichartz inequality associated with the square root of Dunkl Laplacian for the family of orthonormal functions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.01886v2-abstract-full').style.display = 'none'; document.getElementById('2212.01886v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Incomplete and incorrect results</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 42A38; 47B10; Secondary: 42B35; 35P10; 43A32 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.13615">arXiv:2209.13615</a> <span> [<a href="https://arxiv.org/pdf/2209.13615">pdf</a>, <a href="https://arxiv.org/ps/2209.13615">ps</a>, <a href="https://arxiv.org/format/2209.13615">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Sharp Strichartz type estimates for the Schr枚dinger equation associated with harmonic oscillator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Senapati%2C+P+J+K">P Jitendra Kumar Senapati</a>, <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.13615v1-abstract-short" style="display: inline;"> In this article we study the Schr枚dinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates of the spectral projections associated harmonic oscillator proved in \cite{KT}. Our Strichartz type estimates are sharp in sense of regularity of initial data. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.13615v1-abstract-full" style="display: none;"> In this article we study the Schr枚dinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates of the spectral projections associated harmonic oscillator proved in \cite{KT}. Our Strichartz type estimates are sharp in sense of regularity of initial data. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.13615v1-abstract-full').style.display = 'none'; document.getElementById('2209.13615v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.13024">arXiv:2208.13024</a> <span> [<a href="https://arxiv.org/pdf/2208.13024">pdf</a>, <a href="https://arxiv.org/ps/2208.13024">ps</a>, <a href="https://arxiv.org/format/2208.13024">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Strichartz inequality for orthonormal functions associated with Dunkl Laplacian and Hermite-Schr枚dinger operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Senapati%2C+P+J+K">P Jitendra Kumar Senapati</a>, <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.13024v3-abstract-short" style="display: inline;"> Strichartz inequality for the solutions of free Schr枚dinger equation associated with Dunkl Hermite operator $H_魏$ is generalized to any system of orthonormal functions with initial data. A relation between the kernels of Schr枚dinger propagators ($e^{-it H_魏}$ and $e^{it螖_魏}$) associated with the Dunkl Hermite and Dunkl Laplacian operators is established using which corresponding Schtrichartz inequ… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.13024v3-abstract-full').style.display = 'inline'; document.getElementById('2208.13024v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.13024v3-abstract-full" style="display: none;"> Strichartz inequality for the solutions of free Schr枚dinger equation associated with Dunkl Hermite operator $H_魏$ is generalized to any system of orthonormal functions with initial data. A relation between the kernels of Schr枚dinger propagators ($e^{-it H_魏}$ and $e^{it螖_魏}$) associated with the Dunkl Hermite and Dunkl Laplacian operators is established using which corresponding Schtrichartz inequality for orthonormal functions associated with Dunkl Laplacian is obtained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.13024v3-abstract-full').style.display = 'none'; document.getElementById('2208.13024v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:2102.07383 by other authors</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 35Q41; 42B37; Secondary: 42B35; 26D99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.09149">arXiv:2208.09149</a> <span> [<a href="https://arxiv.org/pdf/2208.09149">pdf</a>, <a href="https://arxiv.org/ps/2208.09149">ps</a>, <a href="https://arxiv.org/format/2208.09149">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Operator Algebras">math.OA</span> </div> </div> <p class="title is-5 mathjax"> GD1 inverse and 1GD inverse for Hilbert space operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Sahoo%2C+J+K">Jajati Keshari Sahoo</a>, <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Prdeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Behera%2C+R">Ratikanta Behera</a>, <a href="/search/math?searchtype=author&query=Nashed%2C+M+Z">M. Zuhair Nashed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.09149v1-abstract-short" style="display: inline;"> Mosic and Djordjevic introduced the notation of the gDMP inverse for Hilbert space operators in [J. Spectr. Theory, 8(2):555-573, 2018] by considering generalized Drazin inverse with the Moore-Penrose inverse. This paper introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse for Hilbert space operators. The existence and un… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.09149v1-abstract-full').style.display = 'inline'; document.getElementById('2208.09149v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.09149v1-abstract-full" style="display: none;"> Mosic and Djordjevic introduced the notation of the gDMP inverse for Hilbert space operators in [J. Spectr. Theory, 8(2):555-573, 2018] by considering generalized Drazin inverse with the Moore-Penrose inverse. This paper introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse for Hilbert space operators. The existence and uniqueness of the GD1 (also 1GD) inverse are discussed, along with some properties through core-quasinilpotent decomposition and closed range decomposition operator. We further establish a few explicit representations of the GD1 inverse and their interconnections with generalized Drazin inverse. In addition, we discuss a few properties of GD1 (also 1GD) inverse through binary relation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.09149v1-abstract-full').style.display = 'none'; document.getElementById('2208.09149v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1410.2162">arXiv:1410.2162</a> <span> [<a href="https://arxiv.org/pdf/1410.2162">pdf</a>, <a href="https://arxiv.org/ps/1410.2162">ps</a>, <a href="https://arxiv.org/format/1410.2162">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Mixed norm estimates for the Ces脿ro means associated with Dunkl--Hermite expansions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Roncal%2C+L">L. Roncal</a>, <a href="/search/math?searchtype=author&query=Thangavelu%2C+S">S. Thangavelu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1410.2162v2-abstract-short" style="display: inline;"> Our main goal in this article is to study mixed norm estimates for the Ces脿ro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one consider the Dunkl--Hermite operator (or Dunkl harmonic oscillator) $H_魏:=-螖_魏+|x|^2$, where $螖_魏$ stands for the Dunkl--Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1410.2162v2-abstract-full').style.display = 'inline'; document.getElementById('1410.2162v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1410.2162v2-abstract-full" style="display: none;"> Our main goal in this article is to study mixed norm estimates for the Ces脿ro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one consider the Dunkl--Hermite operator (or Dunkl harmonic oscillator) $H_魏:=-螖_魏+|x|^2$, where $螖_魏$ stands for the Dunkl--Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Ces脿ro means for Laguerre expansions with shifted parameter. In order to obtain the latter, we develop an argument to extend these operators for complex values of the parameters involved and apply a version of three lines lemma. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1410.2162v2-abstract-full').style.display = 'none'; document.getElementById('1410.2162v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 October, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages. Revised version following referee's comments. To appear in Transactions of the American Mathematical Society</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1407.5010">arXiv:1407.5010</a> <span> [<a href="https://arxiv.org/pdf/1407.5010">pdf</a>, <a href="https://arxiv.org/ps/1407.5010">ps</a>, <a href="https://arxiv.org/format/1407.5010">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the chaotic behavior of the Dunkl heat semigroup on weighted $ L^p $ spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Thangavelu%2C+S">S. Thangavelu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1407.5010v1-abstract-short" style="display: inline;"> In this paper we study the chaotic behaviour of the heat semigroup generated by the Dunkl-Laplacian on weighted $ L^p$ spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces $ L^p(\R^n, (\varphi_{i蟻}(x))^2 dx) $ where $ \varphi_{i蟻} $ is the Euclidean spherical function. The behaviour is very similar to the case of the Laplace-Belt… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.5010v1-abstract-full').style.display = 'inline'; document.getElementById('1407.5010v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1407.5010v1-abstract-full" style="display: none;"> In this paper we study the chaotic behaviour of the heat semigroup generated by the Dunkl-Laplacian on weighted $ L^p$ spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces $ L^p(\R^n, (\varphi_{i蟻}(x))^2 dx) $ where $ \varphi_{i蟻} $ is the Euclidean spherical function. The behaviour is very similar to the case of the Laplace-Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.5010v1-abstract-full').style.display = 'none'; document.getElementById('1407.5010v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1407.1644">arXiv:1407.1644</a> <span> [<a href="https://arxiv.org/pdf/1407.1644">pdf</a>, <a href="https://arxiv.org/ps/1407.1644">ps</a>, <a href="https://arxiv.org/format/1407.1644">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Thangavelu%2C+S">S. Thangavelu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1407.1644v1-abstract-short" style="display: inline;"> In this paper we study weighted mixed norm estimates for Riesz transforms associated to Dunkl harmonic oscillators. The idea is to show that the required inequalities are equivalent to certain vector valued inequalities for operator defined in terms of Laguerre expansions. In certain cases the main result can be deduced from the corresponding result for Hermite Riesz transforms. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1407.1644v1-abstract-full" style="display: none;"> In this paper we study weighted mixed norm estimates for Riesz transforms associated to Dunkl harmonic oscillators. The idea is to show that the required inequalities are equivalent to certain vector valued inequalities for operator defined in terms of Laguerre expansions. In certain cases the main result can be deduced from the corresponding result for Hermite Riesz transforms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1407.1644v1-abstract-full').style.display = 'none'; document.getElementById('1407.1644v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 July, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1310.1999">arXiv:1310.1999</a> <span> [<a href="https://arxiv.org/pdf/1310.1999">pdf</a>, <a href="https://arxiv.org/ps/1310.1999">ps</a>, <a href="https://arxiv.org/format/1310.1999">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Revisiting Riesz transforms for Hermite and Special Hermite Operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Boggarapu%2C+P">Pradeep Boggarapu</a>, <a href="/search/math?searchtype=author&query=Thangavelu%2C+S">S. Thangavelu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1310.1999v1-abstract-short" style="display: inline;"> In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of Laguerre functions of different type. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1310.1999v1-abstract-full" style="display: none;"> In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of Laguerre functions of different type. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1310.1999v1-abstract-full').style.display = 'none'; document.getElementById('1310.1999v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 October, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> 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