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2020 Sparse bounds for the discrete spherical maximal functions
Robert Kesler, Michael T. Lacey, Darío Mena
Pure Appl. Anal. 2(1): 75-92 (2020). DOI: 10.2140/paa.2020.2.75

Abstract

We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and Ionescu, is very efficient, and has not been used in the proof of sparse bounds before. The Hardy–Littlewood circle method is used to decompose the multiplier into major and minor arc components. The efficiency arises as one only needs a single estimate on each element of the decomposition.

Citation

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Robert Kesler. Michael T. Lacey. Darío Mena. "Sparse bounds for the discrete spherical maximal functions." Pure Appl. Anal. 2 (1) 75 - 92, 2020. https://doi.org/10.2140/paa.2020.2.75

Information

Received: 8 April 2019; Accepted: 5 July 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159297
MathSciNet: MR4041278
Digital Object Identifier: 10.2140/paa.2020.2.75

Subjects:
Primary: 11K70 , 42B25

Keywords: Discrete , sparse bounds , spherical averages , spherical maximal function

Rights: Copyright © 2020 Mathematical Sciences Publishers

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