Discrete analogues in harmonic analysis - I: l(2) estimates for singular radon transforms

Authors
Stein, EM Wainger, S
Citation
Em. Stein et S. Wainger, Discrete analogues in harmonic analysis - I: l(2) estimates for singular radon transforms, AM J MATH, 121(6), 1999, pp. 1291-1336
Citations number
15
Categorie Soggetti
Mathematics
Journal title
AMERICAN JOURNAL OF MATHEMATICS
ISSN journal
00029327 → ACNP
Volume
121
Issue
6
Year of publication
1999
Pages
1291 - 1336
Database
ISI
SICI code
0002-9327(199912)121:6<1291:DAIHA->2.0.ZU;2-M
Abstract
This paper studies the discrete analogues of singular Radon transforms. We prove the l(2) boundedness for those operators that are "quasi-translation- invariant" The approach used is related to the "circle-method" of Hardy and Littlewood, and requires multi-dimensional extensions of Weyl sums and Gau ss sums, as well as variants that replace scalar sums by operator sums.