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Multiparameter singular integrals and maximal functions

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<a class="author_link" href="/search?&quot;Stein, Elias M.&quot;-c">Stein, Elias M.</a><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --><!-- --> </div> </div> <div style="margin-bottom:10px"> Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 637-670. </div> <div class="binary-file-icon" style="margin-top:20px;margin-bottom:10px"> <div class="wrapper-float"> <div class="d-flex flex-nowrap" style="margin-top:0px"> <a href="/item/10.5802/aif.1304.pdf" target="_blank"> <img src="/static/ptf/img/pdf.svg"> </a> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:20px;margin-bottom:30px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item active"> <a class="nav-link active" lang="fr" data-bs-toggle="tab" data-bs-target="#abstract-fr" href="#abstract-fr"><span title='Français '>Résumé</span></a> </li> <li class="nav-item"> <a class="nav-link" lang="en" data-bs-toggle="tab" data-bs-target="#abstract-en" href="#abstract-en"> <span title='Anglais '>Abstract</span> </a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div lang="fr" id="abstract-fr" class="tab-pane fade show active"> <p>On donne des estimations dans <span class="mathjax-formula" data-tex="$L^p$"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi> <mi>p</mi> </msup></math></span> pour une classe d’opérateurs, à intégrales singulières et maximales, associés à une famille quelconque de dilatations diagonales à <span class="mathjax-formula" data-tex="$k$"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></span> paramètres sur <span class="mathjax-formula" data-tex="${\bf R}^n$"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi mathvariant="bold">R</mi></mrow> <mi>n</mi> </msup></math></span>. Cette classe comprend les opérateurs homogènes définis par noyaux à support sur des variétés homogènes. Pour les intégrales singulières, l’annulation qu’on impose sur le noyau est d’un type “minimal”, défini à partir de la famille de dilatations considérées.</p> </div> <div lang="en" id="abstract-en" class="tab-pane fade"> <p>We prove <span class="mathjax-formula" data-tex="$L^ p$"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi> <mi>p</mi> </msup></math></span>-boundedness for a class of singular integral operators and maximal operators associated with a general <span class="mathjax-formula" data-tex="$k$"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></span>-parameter family of dilations on <span class="mathjax-formula" data-tex="${\bf R}^ n$"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi mathvariant="bold">R</mi></mrow> <mi>n</mi> </msup></math></span>. This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.</p> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:10px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#info-tab" href="#info-tab">Détail</a></li> <li class="nav-item"><a class="nav-link" data-bs-toggle="tab"data-bs-target="#citation-tab" href="#citation-tab">Export</a></li> <li class="nav-item"> <a class="nav-link " data-bs-toggle="tab" data-toggle="tab" data-bs-target="#how-to-cite-tab" href="#how-to-cite-tab">Comment citer</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="info-tab" class="tab-pane fade show active"> <!--Mis en ligne le : <time datetime="2024-03-10">2024-03-10</time><br>--> <div style="margin-top:5px"> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=94d:42020" class="badge bg-secondary rounded-pill ref-badge extid-badge"> MR </a> &nbsp; <a href="https://zbmath.org/?q=an:0760.42008" class="badge bg-secondary rounded-pill ref-badge extid-badge"> Zbl </a> </div> DOI : <a href="https://doi.org/10.5802/aif.1304">10.5802/aif.1304</a> <br> <div style="margin-top:5px"> </div> <div style="margin-top:5px"> </div> </div> <div id="citation-tab" class="tab-pane fade"> <div class="upper"> <ul class="nav nav-pills"> <li role="presentation" class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#bibtex" href="#bibtex">BibTeX</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#ris" href="#ris">RIS</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#enw" href="#enw">EndNote</a></li> </ul> <div class="tab-content"> <div id="bibtex" class="tab-pane fade show active"> <pre class="upper-right-content" id="bibtex-div">@article{AIF_1992__42_3_637_0, author = {Ricci, Fulvio and Stein, Elias M.}, title = {Multiparameter singular integrals and maximal functions}, journal = {Annales de l&#x27;Institut Fourier}, pages = {637--670}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {3}, year = {1992}, doi = {10.5802/aif.1304}, zbl = {0760.42008}, mrnumber = {94d:42020}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1304/} }</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#bibtex-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/export_citation/AIF_1992__42_3_637_0/bib/"></a> </div> <div id="ris" class="tab-pane fade"> <pre class="upper-right-content" id="ris-div">TY - JOUR AU - Ricci, Fulvio AU - Stein, Elias M. TI - Multiparameter singular integrals and maximal functions JO - Annales de l&#x27;Institut Fourier PY - 1992 SP - 637 EP - 670 VL - 42 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1304/ DO - 10.5802/aif.1304 LA - en ID - AIF_1992__42_3_637_0 ER - </pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#ris-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/export_citation/AIF_1992__42_3_637_0/ris/"></a> </div> <div id="enw" class="tab-pane fade"> <pre class="upper-right-content" id="enw-div">%0 Journal Article %A Ricci, Fulvio %A Stein, Elias M. %T Multiparameter singular integrals and maximal functions %J Annales de l&#x27;Institut Fourier %D 1992 %P 637-670 %V 42 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1304/ %R 10.5802/aif.1304 %G en %F AIF_1992__42_3_637_0</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#enw-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="Télécharger" href="/export_citation/AIF_1992__42_3_637_0/enw/"></a> </div> </div> </div> </div> <div id="how-to-cite-tab" class="tab-pane fade "> <div class="upper-right"> <pre class="upper-right-content" id="how-to-cite-div">Ricci, Fulvio; Stein, Elias M. Multiparameter singular integrals and maximal functions. Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 637-670. doi : 10.5802/aif.1304. https://aif.centre-mersenne.org/articles/10.5802/aif.1304/</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#how-to-cite-div" aria-hidden="true" title="Copier dans le presse-papier"></button> </div> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:30px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab" > <li class="nav-item" id="main-citations-li" > <a class="nav-link active" data-bs-toggle="tab" data-bs-target="#references-tab" href="#references-tab">Bibliographie</a> </li> <li class="nav-item" id="citations-html" style="display:none"> <a class="nav-link" data-bs-toggle="tab" data-bs-target="#citations-tab" href="#citations-tab">Cité par</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="references-tab" class="tab-pane fade show active"> <div style="margin-top:11px;margin-bottom: 0px"> <p class="bibitemcls " > [1] <span class="citation-author">A. 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