Document Zbl 07888067

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Sin., Engl. Ser.</a> <a href="/?q=in%3A515474" title="Articles in this Issue">40, No. 6, 1533-1562 (2024)</a>. </div> <div class="abstract">Summary: In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on $\mathcal{H}_{\alpha, 2}^r$ are proven with the help of the Weinstein transform technique.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7888067">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47G30" title="MSC2020">47G30</a> </td> <td class="space"> Pseudodifferential operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A44A15" title="MSC2020">44A15</a> </td> <td class="space"> Special integral transforms (Legendre, Hilbert, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46F12" title="MSC2020">46F12</a> </td> <td class="space"> Integral transforms in distribution spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35S05" title="MSC2020">35S05</a> </td> <td class="space"> Pseudodifferential operators as generalizations of partial differential operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apseudo-differential+operators">pseudo-differential operators</a>; <a href="/?q=ut%3Ahomogeneous+symbol+class">homogeneous symbol class</a>; <a href="/?q=ut%3AWeinstein+operator">Weinstein operator</a>; <a href="/?q=ut%3ASobolev+space">Sobolev space</a>; <a href="/?q=ut%3AWeinstein+transform">Weinstein transform</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 07888067" data-ciurl="/ci/07888067" data-biburl="/bibtex/07888067.bib" data-amsurl="/amsrefs/07888067.bib" data-xmlurl="/xml/07888067.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07888067.pdf" title="Zbl 07888067 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/s10114-024-2405-x" aria-label="DOI for “Pseudo-differential operators of homogeneous symbol class associated with the Weinstein transform”" title="10.1007/s10114-024-2405-x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bényi, Á.; Bownik, M., Anisotropic classes of homogeneous pseudodifferential symbols, Mathematics, 200, 1, 41-66, 2010 · <a href="/1215.47038" class="nowrap">Zbl 1215.47038</a></td> </tr><tr> <td>[2]</td> <td class="space">Chettaoui, C.; Trimèche, K., Bochner-Hecke theorems for the Weinstein transform and application, Fractional Calculus and Applied Analysis, 13, 261-280, 2010 · <a href="/1226.42006" class="nowrap">Zbl 1226.42006</a></td> </tr><tr> <td>[3]</td> <td class="space">Cardona, D.; del Corral, C.; Kumar, V., Dixmier traces for discrete pseudo-differential operators, J. 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