Discrete analogues of singular Radon transforms

E. M. Stein, Stephen Wainger

Type: Article

Publication Date: 1990-01-01

Citations: 53

DOI: https://doi.org/10.1090/s0273-0979-1990-15973-7

Abstract

The purpose of this paper is to describe recent results we have obtained in finding discrete analogues of the theory of singular integrals on curves, or more generally of "singular Radon transforms," at least in the translation-invariant case.Our theorems are related to estimates for certain exponential sums that arise in number theory; they are also connected with Bourgain's recent maximal ergodic theorem [2,3].The detailed proofs of our results are quite lengthy, and will appear elsewhere.Here we shall limit ourselves to stating the main conclusions, and sketching the motivation and background.We take this opportunity to acknowledge our indebtedness to Guido Weiss and A. De la Torre, whose suggestions were the starting point of this research.

Locations

Project Euclid (Cornell University) - View - PDF
Bulletin of the American Mathematical Society - View - PDF

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