dc.contributor.author |
Vitturi, Marco |
|
dc.contributor.author |
Wright, James |
|
dc.date.accessioned |
2020-09-23T12:06:52Z |
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dc.date.available |
2020-09-23T12:06:52Z |
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dc.date.issued |
2020-05-26 |
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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 |
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dc.identifier.startpage |
5439 |
en |
dc.identifier.endpage |
5465 |
en |
dc.identifier.issn |
0002-9947 |
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dc.identifier.uri |
http://hdl.handle.net/10468/10574 |
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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. |
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dc.format.mimetype |
application/pdf |
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dc.language.iso |
en |
en |
dc.publisher |
American Mathematical Society |
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dc.rights |
© 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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dc.rights.uri |
https://creativecommons.org/licenses/by-nc-nd/4.0/ |
en |
dc.subject |
Double Hilbert transforms |
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dc.subject |
Radon transforms |
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dc.subject |
Polynomial surfaces |
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dc.subject |
Harmonic analysis |
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dc.subject |
Nilpotent groups |
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dc.subject |
Kernels |
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dc.title |
Multiparameter singular integrals on the Heisenberg group: uniform estimates |
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dc.type |
Article (peer-reviewed) |
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dc.internal.authorcontactother |
Marco Vitturi, Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: marco.vitturi@ucc.ie |
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dc.internal.availability |
Full text available |
en |
dc.date.updated |
2020-09-23T11:53:02Z |
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dc.description.version |
Accepted Version |
en |
dc.internal.rssid |
530301733 |
|
dc.internal.wokid |
WOS:000551418100006 |
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dc.description.status |
Peer reviewed |
en |
dc.identifier.journaltitle |
Transactions of the American Mathematical Society |
en |
dc.internal.copyrightchecked |
Yes |
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dc.internal.licenseacceptance |
Yes |
en |
dc.internal.IRISemailaddress |
marco.vitturi@ucc.ie |
en |
dc.identifier.eissn |
1088-6850 |
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