Document Zbl 1160.42009

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Math.</a> <a href="/?q=in%3A245307" title="Articles in this Issue">220, No. 4, 1222-1264 (2009)</a>. </div> <div class="abstract">Authors’ abstract: A multi(sub)linear maximal operator that acts on the product of $m$ Lebesgue spaces and is smaller than the $m$-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón-Zygmund operators with $BMO$ functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A2794">Niels Jacob (Swansea)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A5518758">Cited in <strong>21</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A5518758">Cited in <strong>317</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B20" title="MSC2020">42B20</a> </td> <td class="space"> Singular and oscillatory integrals (Calderón-Zygmund, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B25" title="MSC2020">42B25</a> </td> <td class="space"> Maximal functions, Littlewood-Paley theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amultilinear+singular+integrals">multilinear singular integrals</a>; <a href="/?q=ut%3ACalder%C3%B3n-Zygmund+theory">Calderón-Zygmund theory</a>; <a href="/?q=ut%3Amaximal+operators">maximal operators</a>; <a href="/?q=ut%3Aweighted+norm+inequalities">weighted norm inequalities</a>; <a href="/?q=ut%3Acommutators">commutators</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 1160.42009" data-ciurl="/ci/05518758" data-biburl="/bibtex/05518758.bib" data-amsurl="/amsrefs/05518758.bib" data-xmlurl="/xml/05518758.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05518758.pdf" title="Zbl 1160.42009 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/10.1016/j.aim.2008.10.014" aria-label="DOI for “New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory”" title="10.1016/j.aim.2008.10.014">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/11336/79548" 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">Alvarez, J.; Pérez, C., Estimates with $A_\infty$ weights for various singular integral operators, Boll. 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