Document Zbl 1513.42026

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Sci., Ser. B, Engl. Ed.</a> <a href="/?q=in%3A484379" title="Articles in this Issue">41, No. 3, 968-990 (2021)</a>. </div> <div class="abstract">Summary: As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from $\mathcal{C}_0(\mathbb{H}^n)\times L^2(\mathbb{H}^n)$ to $L^2(\mathbb{H}^n)$, from $L^2(\mathbb{H}^n)\times\mathcal{C}_0(\mathbb{H}^n)$ to $L^2(\mathbb{H}^n)$, and from $L^p \times L^q$ to $L^r$ with $2 < p$, $q < \infty$, $2 \leq r \leq \infty$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7557587">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B15" title="MSC2020">42B15</a> </td> <td class="space"> Multipliers for harmonic analysis in several variables </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A43A80" title="MSC2020">43A80</a> </td> <td class="space"> Analysis on other specific Lie groups </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Abilinear+spectral+multipliers">bilinear spectral multipliers</a>; <a href="/?q=ut%3AHeisenberg+groups">Heisenberg groups</a>; <a href="/?q=ut%3Aboundedness">boundedness</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 1513.42026" data-ciurl="/ci/07557587" data-biburl="/bibtex/07557587.bib" data-amsurl="/amsrefs/07557587.bib" data-xmlurl="/xml/07557587.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07557587.pdf" title="Zbl 1513.42026 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/s10473-021-0321-z" aria-label="DOI for “Bilinear spectral multipliers on Heisenberg groups”" title="10.1007/s10473-021-0321-z">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">Alexopoulos, G., Spectral multipliers on Lie groups of polynomial growth, Proc Amer Math Soc, 120, 3, 973-979 (1994) · <a href="/0794.43003" class="nowrap">Zbl 0794.43003</a></td> </tr><tr> <td>[2]</td> <td class="space">Bahouri, H.; Fermanian, K. 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