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Sparse bounds for the
discrete spherical maximal functions
Robert Kesler, Michael T. Lacey and Darío Mena |
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Vol. 2 (2020), No. 1, 75–92
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Abstract |
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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. |
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Keywords
sparse bounds, spherical averages, discrete, spherical
maximal function
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Mathematical Subject Classification 2010
Primary: 11K70, 42B25
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Milestones
Received: 8 April 2019
Accepted: 5 July 2019
Published: 9 November 2019
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Authors |
| Robert Kesler | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Michael T. Lacey | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Darío Mena | |
| Escuela de Matemática Universidad de Costa Rica San José Costa Rica |
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