Document Zbl 1478.46026

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Math. Anal.</a> <a href="/?q=in%3A463985" title="Articles in this Issue">15, No. 3, Paper No. 46, 27 p. (2021)</a>. </div> <div class="abstract">Summary: In this paper, we will use the convex modular $\rho^*(f)$ to investigate $\Vert f\Vert_{\Psi ,q}^*$ on $(L_{\Phi })^*$ defined by the formula $\Vert f\Vert_{\Psi ,q}^*=\inf_{k>0}\frac{1}{k}s_q(\rho^*(kf))$, which is the norm formula in Orlicz dual spaces equipped with $p$-Amemiya norm. The attainable points of dual norm $\Vert f\Vert_{\Psi ,q}^*$ are discussed, the interval for dual norm $\Vert f\Vert_{\Psi ,q}^*$ attainability is described. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points. As a result, criteria for smoothness of $L_{\Phi ,p}$ $(1\le p\le \infty )$ is also obtained. The obtained results unify, complete and extended as well the results presented by a number of papers devoted to studying the smoothness of Orlicz spaces endowed with the Luxemburg norm and the Orlicz norm separately.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7354433">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A46E30" title="MSC2020">46E30</a> </td> <td class="space"> Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46B20" title="MSC2020">46B20</a> </td> <td class="space"> Geometry and structure of normed linear spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46B45" title="MSC2020">46B45</a> </td> <td class="space"> Banach sequence spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46B42" title="MSC2020">46B42</a> </td> <td class="space"> Banach lattices </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46A80" title="MSC2020">46A80</a> </td> <td class="space"> Modular spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AOrlicz+space">Orlicz space</a>; <a href="/?q=ut%3A%5C%28p%5C%29-Amemiya+norm">$p$-Amemiya norm</a>; <a href="/?q=ut%3Asupporting+functional">supporting functional</a>; <a href="/?q=ut%3Asmooth+point">smooth point</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1478.46026" data-ciurl="/ci/07354433" data-biburl="/bibtex/07354433.bib" data-amsurl="/amsrefs/07354433.bib" data-xmlurl="/xml/07354433.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07354433.pdf" title="Zbl 1478.46026 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s43037-021-00133-x" aria-label="DOI for “Smoothness of Orlicz function spaces equipped with the $p$-Amemiya norm”" title="10.1007/s43037-021-00133-x">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aliprantis, CD; Burkinshaw, O., Positive Operators (1985), Springer · <a href="/0608.47039" class="nowrap">Zbl 0608.47039</a></td> </tr><tr> <td>[2]</td> <td class="space">Ando, T., Linear functionals on Orlicz spaces, Nieuw Arch. Wiskd., 8, 8, 1-16 (1960) · <a href="/0129.08001" class="nowrap">Zbl 0129.08001</a></td> </tr><tr> <td>[3]</td> <td class="space">Chen, L.; Cui, Y., Complex extreme points and complex rotundity in Orlicz function spaces equipped with the p-Amemiya norm, Nonlinear Anal., 73, 5, 1389-1393 (2010) · <a href="/1210.46013" class="nowrap">Zbl 1210.46013</a> · <a href="https://doi.org/10.1016/j.na.2010.04.071" class="nowrap">doi:10.1016/j.na.2010.04.071</a></td> </tr><tr> <td>[4]</td> <td class="space">Chen, S., Smoothness of Orlicz spaces, Comment. Math., XXVII, 49-58 (1987) · <a href="/0641.46010" class="nowrap">Zbl 0641.46010</a></td> </tr><tr> <td>[5]</td> <td class="space">Chen, S., The smooth point of Orlicz spaces, Nat. Sci. J. Harbin Norm. Univ., 5, 1-4 (1989) · <a href="/0971.46510" class="nowrap">Zbl 0971.46510</a></td> </tr><tr> <td>[6]</td> <td class="space">Chen, S.: Geometry of Orlicz spaces. Diss. Math. 365 (1996) · <a href="/1089.46500" class="nowrap">Zbl 1089.46500</a></td> </tr><tr> <td>[7]</td> <td class="space">Chen, S.; Hudzik, H.; Kaminska, A., Support functionals and smooth points in Orlicz function spaces equipped with the Orlicz norm, Math. Jpn., 39, 2, 271-279 (1994) · <a href="/0804.46035" class="nowrap">Zbl 0804.46035</a></td> </tr><tr> <td>[8]</td> <td class="space">Cui, Y.; Hudzik, H.; Wisla, M.; Wlazlak, K., Non-squareness properties of Orlicz spaces equipped with the p-Amemiya norm, Nonlinear Anal. Theory Methods Appl., 75, 10, 3973-3993 (2012) · <a href="/1247.46015" class="nowrap">Zbl 1247.46015</a> · <a href="https://doi.org/10.1016/j.na.2012.02.014" class="nowrap">doi:10.1016/j.na.2012.02.014</a></td> </tr><tr> <td>[9]</td> <td class="space">Cui, Y.; Duan, L.; Hudzik, H.; Wisla, M., Basic theory of p-Amemiya norm in Orlicz spaces: extreme points and rotundity in Orlicz spaces endowed with these norms, Nonlinear Anal., 69, 5-6, 1796-1816 (2008) · <a href="/1165.46005" class="nowrap">Zbl 1165.46005</a> · <a href="https://doi.org/10.1016/j.na.2007.07.026" class="nowrap">doi:10.1016/j.na.2007.07.026</a></td> </tr><tr> <td>[10]</td> <td class="space">Cui, Y.; Hudzik, H.; Li, J., Some fundamental properties for duals of Orlicz spaces, Nonlinear Anal. Theory Methods Appl., 73, 8, 2353-2360 (2010) · <a href="/1211.46010" class="nowrap">Zbl 1211.46010</a> · <a href="https://doi.org/10.1016/j.na.2010.05.010" class="nowrap">doi:10.1016/j.na.2010.05.010</a></td> </tr><tr> <td>[11]</td> <td class="space">Cui, Y.; Hudzik, H.; Li, J.; Wisla, M., Strongly extreme points in Orlicz spaces equipped with the p-Amemiya norm, Nonlinear Anal., 71, 6343-6364 (2009) · <a href="/1186.46015" class="nowrap">Zbl 1186.46015</a> · <a href="https://doi.org/10.1016/j.na.2009.06.085" class="nowrap">doi:10.1016/j.na.2009.06.085</a></td> </tr><tr> <td>[12]</td> <td class="space">Cui, Y.; Hudzik, H.; Wisla, M., Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the p-Amemiya norm, J. Math. Anal. Appl., 432, 2, 1095-1105 (2015) · <a href="/1321.41049" class="nowrap">Zbl 1321.41049</a> · <a href="https://doi.org/10.1016/j.jmaa.2015.07.004" class="nowrap">doi:10.1016/j.jmaa.2015.07.004</a></td> </tr><tr> <td>[13]</td> <td class="space">Grzaślewicz, R.; Hudzik, H., Smooth points of Orlicz spaces equipped with Luxemburg norm, Math. Nachr., 155, 1, 31-45 (1992) · <a href="/0795.46016" class="nowrap">Zbl 0795.46016</a> · <a href="https://doi.org/10.1002/mana.19921550104" class="nowrap">doi:10.1002/mana.19921550104</a></td> </tr><tr> <td>[14]</td> <td class="space">He, X.; Cui, Y.; Hudzik, H., The fixed point property of Orlicz sequence spaces equipped with the p-Amemiya norm, Fixed Point Theory Appl, 2013, 1, 1-18 (2013) · <a href="/1423.47055" class="nowrap">Zbl 1423.47055</a> · <a href="https://doi.org/10.1186/1687-1812-2013-1" class="nowrap">doi:10.1186/1687-1812-2013-1</a></td> </tr><tr> <td>[15]</td> <td class="space">Hudzik, H.; Maligranda, L., Amemiya norm equals Orlicz norm in general, Indag. Math., 11, 4, 573-585 (2000) · <a href="/1010.46031" class="nowrap">Zbl 1010.46031</a> · <a href="https://doi.org/10.1016/S0019-3577(00)80026-9" class="nowrap">doi:10.1016/S0019-3577(00)80026-9</a></td> </tr><tr> <td>[16]</td> <td class="space">Hudzik, H.; Zbaszyniak, Z., Smoothness in Musielak-Orlicz spaces equipped with Orlicz norm, Collect. Math., 48, 8-9, 543-561 (1997) · <a href="/0904.46018" class="nowrap">Zbl 0904.46018</a></td> </tr><tr> <td>[17]</td> <td class="space">Kaczmarek, R., Uniform rotundity of Orlicz function spaces equipped with the p-Amemiya norm, Math. Nachr., 291, 10, 1514-1532 (2018) · <a href="/1423.46023" class="nowrap">Zbl 1423.46023</a> · <a href="https://doi.org/10.1002/mana.201700025" class="nowrap">doi:10.1002/mana.201700025</a></td> </tr><tr> <td>[18]</td> <td class="space">Krasnoselskii, MA; Rutickii, YB, Convex Functions and Orlicz Spaces (1961), P. Noordhoff Ltd · <a href="/0095.09103" class="nowrap">Zbl 0095.09103</a></td> </tr><tr> <td>[19]</td> <td class="space">Li, X.; Cui, Y., The dual space of Orlicz space equipped with p-Amemiya norm, J. Harbin Univ. Sci. Technol., 16, 1, 110-112 (2011)</td> </tr><tr> <td>[20]</td> <td class="space">Luxemburg, WAJ; Zaanen, AC, Conjugate spaces of Orlicz spaces, Indag. Math., 59, 217-228 (1956) · <a href="/0072.12301" class="nowrap">Zbl 0072.12301</a> · <a href="https://doi.org/10.1016/S1385-7258(56)50029-7" class="nowrap">doi:10.1016/S1385-7258(56)50029-7</a></td> </tr><tr> <td>[21]</td> <td class="space">Musielak, J., Orlicz Spaces and Modular Spaces (1983), Springer · <a href="/0557.46020" class="nowrap">Zbl 0557.46020</a> · <a href="https://doi.org/10.1007/BFb0072210" class="nowrap">doi:10.1007/BFb0072210</a></td> </tr><tr> <td>[22]</td> <td class="space">Musielak, J.; Orlicz, W., On modular spaces, Stud. Math., 18, 1, 1-128 (1959) · <a href="/0085.32301" class="nowrap">Zbl 0085.32301</a> · <a href="https://doi.org/10.4064/sm-18-1-1-9" class="nowrap">doi:10.4064/sm-18-1-1-9</a></td> </tr><tr> <td>[23]</td> <td class="space">Nakano, H., Topology and Linear Topological Spaces (1951), Maruzen Co.Ltd</td> </tr><tr> <td>[24]</td> <td class="space">Orlicz, W., A note on modular spaces, Bull. Acad. Pol. Sci. Math. Astron. Phys., 9, 157-162 (1961) · <a href="/0109.33404" class="nowrap">Zbl 0109.33404</a></td> </tr><tr> <td>[25]</td> <td class="space">Rao, MM; Ren, Z., Theory of Orlicz Spaces (1991), Marcek Dekker Inc · <a href="/0724.46032" class="nowrap">Zbl 0724.46032</a></td> </tr><tr> <td>[26]</td> <td class="space">Shi, Z.; Wang, T., On the smoothness of Orlicz sequence spaces equipped with Orlicz norm, Collect. Math., 47, 2, 105-109 (1996) · <a href="/0866.46004" class="nowrap">Zbl 0866.46004</a></td> </tr><tr> <td>[27]</td> <td class="space">Vigelis, RF; Cavalcante, CC, Smoothness of the Orlicz norm in Musielak-Orlicz function spaces, Math. Nachr., 287, 8-9, 1025-1041 (2014) · <a href="/1309.46004" class="nowrap">Zbl 1309.46004</a> · <a href="https://doi.org/10.1002/mana.201200214" class="nowrap">doi:10.1002/mana.201200214</a></td> </tr><tr> <td>[28]</td> <td class="space">Wang, B.; Zhang, Y., The smooth points of Orlicz sequence spaces, Nat. Sci. J. Harbin Norm. Univ., 7, 3, 18-22 (1991) · <a href="/0971.46508" class="nowrap">Zbl 0971.46508</a></td> </tr><tr> <td>[29]</td> <td class="space">Wisla, M., Geometric properties of Orlicz spaces equipped with the p-Amemiya norms-results and open questions, Comment. Math., 55, 183-209 (2015) · <a href="/1362.46034" class="nowrap">Zbl 1362.46034</a></td> </tr><tr> <td>[30]</td> <td class="space">Wisla, M., Orlicz spaces equipped with the s-norms, J. Math. Anal. Appl., 483, 2, 1-30 (2020) · <a href="/1446.46014" class="nowrap">Zbl 1446.46014</a> · <a href="https://doi.org/10.1016/j.jmaa.2019.123659" class="nowrap">doi:10.1016/j.jmaa.2019.123659</a></td> </tr><tr> <td>[31]</td> <td class="space">Wu, C.; Wang, T.; Chen, S.; Wang, Y., Geometric Theory of Orlicz Spaces (1986), Print House</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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