Discrete analogues in harmonic analysis -: I:: l2 estimates for singular radon transforms

被引：54

作者：

Stein, EM ^{[1
]}

Wainger, S

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 1999年 / 121卷 / 06期

关键词：

D O I：

10.1353/ajm.1999.0046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Gauss sums, as well as variants that replace scalar sums by operator sums.

引用

页码：1291 / 1336

页数：46

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