Multiparameter singular integrals on the Heisenberg group: uniform estimates

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dc.contributor.author Vitturi, Marco
dc.contributor.author Wright, James
dc.date.accessioned 2020-09-23T12:06:52Z
dc.date.available 2020-09-23T12:06:52Z
dc.date.issued 2020-05-26
dc.identifier.citation Vitturi, M. and Wright, J. (2020) 'Multiparameter singular integrals on the Heisenberg group: uniform estimates', Transactions of the American Mathematical Society, 373, pp. 5439-5465. doi: 10.1090/tran/8079 en
dc.identifier.volume 373 en
dc.identifier.startpage 5439 en
dc.identifier.endpage 5465 en
dc.identifier.issn 0002-9947
dc.identifier.uri http://hdl.handle.net/10468/10574
dc.identifier.doi 10.1090/tran/8079 en
dc.description.abstract We consider a class of multiparameter singular Radon integral operators on the Heisenberg group H-1 where the underlying submanifold is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg convolution is replaced by euclidean convolution, is that the operators on the Heisenberg group are always L-2 bounded. This is not the case in the euclidean setting where L-2 boundedness depends on the polynomial defining the underlying surface. Here we uncover some new, interesting phenomena. For example, although the Heisenberg group operators are always L-2 bounded, the bounds are not uniform in the coefficients of polynomials with fixed degree. When we ask for which polynomials uniform L-2 bounds hold, we arrive at the same class where uniform bounds hold in the euclidean case. en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher American Mathematical Society en
dc.rights © 2020, American Mathematical Society. First published by the American Mathematical Society in Transactions of the American Mathematical Society, 373, May 2020. en
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/ en
dc.subject Double Hilbert transforms en
dc.subject Radon transforms en
dc.subject Polynomial surfaces en
dc.subject Harmonic analysis en
dc.subject Nilpotent groups en
dc.subject Kernels en
dc.title Multiparameter singular integrals on the Heisenberg group: uniform estimates en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Marco Vitturi, Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: marco.vitturi@ucc.ie en
dc.internal.availability Full text available en
dc.date.updated 2020-09-23T11:53:02Z
dc.description.version Accepted Version en
dc.internal.rssid 530301733
dc.internal.wokid WOS:000551418100006
dc.description.status Peer reviewed en
dc.identifier.journaltitle Transactions of the American Mathematical Society en
dc.internal.copyrightchecked Yes
dc.internal.licenseacceptance Yes en
dc.internal.IRISemailaddress marco.vitturi@ucc.ie en
dc.identifier.eissn 1088-6850


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© 2020, American Mathematical Society. First published by the American Mathematical Society in Transactions of the American Mathematical Society, 373, May 2020. Except where otherwise noted, this item's license is described as © 2020, American Mathematical Society. First published by the American Mathematical Society in Transactions of the American Mathematical Society, 373, May 2020.
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