Document Zbl 1340.31009

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Math. J.</a> <a href="/?q=in%3A340663" title="Articles in this Issue">64, No. 1, 209-228 (2014)</a>. </div> <div class="abstract">Summary: Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev’s inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger’s inequality and the continuity for Riesz potentials.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6391488">Cited in <strong>10</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A31B15" title="MSC2020">31B15</a> </td> <td class="space"> Potentials and capacities, extremal length and related notions in higher dimensions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46E35" title="MSC2020">46E35</a> </td> <td class="space"> Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Agrand+Morrey+space">grand Morrey space</a>; <a href="/?q=ut%3Avariable+exponent">variable exponent</a>; <a href="/?q=ut%3Anon-doubling+measure">non-doubling measure</a>; <a href="/?q=ut%3Ametric+measure+space">metric measure space</a>; <a href="/?q=ut%3ARiesz+potential">Riesz potential</a>; <a href="/?q=ut%3Amaximal+operator">maximal operator</a>; <a href="/?q=ut%3ASobolev%27s+inequality">Sobolev’s inequality</a>; <a href="/?q=ut%3ATrudinger%27s+exponential+inequality">Trudinger’s exponential inequality</a>; <a href="/?q=ut%3Acontinuity">continuity</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 1340.31009" data-ciurl="/ci/06391488" data-biburl="/bibtex/06391488.bib" data-amsurl="/amsrefs/06391488.bib" data-xmlurl="/xml/06391488.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06391488.pdf" title="Zbl 1340.31009 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/s10587-014-0095-8" aria-label="DOI for “Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces.”" title="10.1007/s10587-014-0095-8">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/10338.dmlcz/143961" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">D. 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