Square function estimates for discrete Radon transforms

Mirek, Mariusz

doi:10.2140/apde.2018.11.583

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Square function estimates for discrete Radon transforms

Mariusz Mirek

Vol. 11 (2018), No. 3, 583–608

DOI: 10.2140/apde.2018.11.583

Abstract

We show $ℓ^{p} (ℤ^{d})$ -boundedness, for $p \in (1, \infty)$ , 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

Vol. 11, No. 3, 2018