Document Zbl 1402.46023

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J. Math.</a> <a href="/?q=in%3A406621" title="Articles in this Issue">15, No. 3, Paper No. 100, 15 p. (2018)</a>. </div> <div class="abstract">Summary: In this note some structural properties of grand variable exponent Lebesgue/Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of $L^{\infty}$ and the closure of $L^{p(\cdot ), \lambda (\cdot)}$ in grand variable exponent Morrey space $L^{p(\cdot), \lambda (\cdot), \theta}$ coincide if the measure of the underlying space is finite. Moreover, we get two different characterizations of this class. Further, duality and preduality of grand variable exponent Lebesgue spaces defined on quasi-metric measure spaces with $\sigma $-finite measure are obtained, which is new even when $\mu $ is finite.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6909939">Cited in <strong>14</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%3A46B10" title="MSC2020">46B10</a> </td> <td class="space"> Duality and reflexivity in normed linear and Banach spaces </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMorrey+spaces">Morrey spaces</a>; <a href="/?q=ut%3ANakano+spaces">Nakano spaces</a>; <a href="/?q=ut%3AIwaniec-Sbordone+space">Iwaniec-Sbordone space</a>; <a href="/?q=ut%3Agrand+variable+exponent+Morrey+spaces">grand variable exponent Morrey spaces</a>; <a href="/?q=ut%3Adensity">density</a>; <a href="/?q=ut%3Aclass+of+bounded+functions">class of bounded functions</a>; <a href="/?q=ut%3Apredual+space">predual space</a>; <a href="/?q=ut%3Adual+space">dual space</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 1402.46023" data-ciurl="/ci/06909939" data-biburl="/bibtex/06909939.bib" data-amsurl="/amsrefs/06909939.bib" data-xmlurl="/xml/06909939.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06909939.pdf" title="Zbl 1402.46023 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/s00009-018-1145-5" aria-label="DOI for “Density, duality and preduality in grand variable exponent Lebesgue and Morrey spaces”" title="10.1007/s00009-018-1145-5">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1710.02383"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aboulaich, R; Meskine, D; Souissi, A, New disscusion models in image processing, Comput. 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