Multiparameter singular integrals on the Heisenberg group: uniform estimates
| 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.date.updated | 2020-09-23T11:53:02Z | |
| 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.description.status | Peer reviewed | en |
| dc.description.version | Accepted Version | en |
| dc.format.mimetype | application/pdf | en |
| 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.doi | 10.1090/tran/8079 | en |
| dc.identifier.eissn | 1088-6850 | |
| dc.identifier.endpage | 5465 | en |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.journaltitle | Transactions of the American Mathematical Society | en |
| dc.identifier.startpage | 5439 | en |
| dc.identifier.uri | https://hdl.handle.net/10468/10574 | |
| dc.identifier.volume | 373 | 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 |
