Vol. 11, No. 3, 2018

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Square function estimates for discrete Radon transforms

Mariusz Mirek

Vol. 11 (2018), No. 3, 583–608
Abstract

We show p(d)-boundedness, for p (1,), of discrete singular integrals of Radon type with the aid of appropriate square function estimates, which can be thought of as a discrete counterpart of Littlewood–Paley theory. It is a very robust approach which allows us to proceed as in the continuous case.

Keywords
discrete harmonic analysis, Radon operators, Hardy–Littlewood circle method, exponential sums
Mathematical Subject Classification 2010
Primary: 11L07, 42B20, 42B25
Milestones
Received: 18 June 2016
Revised: 22 July 2017
Accepted: 20 September 2017
Published: 22 November 2017
Authors
Mariusz Mirek
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States
Instytut Matematyczny
Uniwersytet Wrocławski
Wrocław
Poland