Document Zbl 1511.46021

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Math. Anal.</a> <a href="/?q=in%3A489799" title="Articles in this Issue">17, No. 1, Paper No. 7, 22 p. (2023)</a>. </div> <div class="abstract">Summary: In this paper, we give criteria for the relatively compact sets of Banach space-valued bounded-variation spaces in the sense of Jordan and Banach space-valued bounded Wiener $p$-variation spaces as $p\in (0,1)$. Then, we give sufficient conditions for the relatively compact sets of others Banach space-valued bounded variation spaces, such as Banach space-valued bounded Wiener $p$-variation spaces as $p\in (1,\infty)$, Banach space-valued bounded Wiener-Young variation spaces, Banach space-valued bounded Schramm variation spaces, Banach space-valued bounded Waterman variation spaces, Banach space-valued bounded Riesz variation spaces, and Banach space-valued bounded Korenblum variation spaces.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7629842">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%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%3A46B50" title="MSC2020">46B50</a> </td> <td class="space"> Compactness in Banach (or normed) spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46E40" title="MSC2020">46E40</a> </td> <td class="space"> Spaces of vector- and operator-valued functions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A45" title="MSC2020">26A45</a> </td> <td class="space"> Functions of bounded variation, generalizations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arelatively+compact+set">relatively compact set</a>; <a href="/?q=ut%3Abounded-variation+space">bounded-variation space</a>; <a href="/?q=ut%3Aequivariated">equivariated</a>; <a href="/?q=ut%3ABanach+space-valued+space">Banach space-valued 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 1511.46021" data-ciurl="/ci/07629842" data-biburl="/bibtex/07629842.bib" data-amsurl="/amsrefs/07629842.bib" data-xmlurl="/xml/07629842.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07629842.pdf" title="Zbl 1511.46021 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/s43037-022-00230-5" aria-label="DOI for “Relatively compact sets of Banach space-valued bounded-variation spaces”" title="10.1007/s43037-022-00230-5">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">Appell, J.; Banas, J.; Merentes, N., Bounded Variation and Around (2013), Berlin: De Gruyter, Berlin · <a href="/1282.26001" class="nowrap">Zbl 1282.26001</a> · <a href="https://doi.org/10.1515/9783110265118" class="nowrap">doi:10.1515/9783110265118</a></td> </tr><tr> <td>[2]</td> <td class="space">Bourdaud, G.; Cristoforis, ML; Sickel, W., Superposition operators and functions of bounded p-variation, Rev. 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