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Robert Kesler,
Michael T. Lacey, and Darío Mena Arias
Lacunary discrete spherical maximal functions
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| Published: |
June 20, 2019. |
| Keywords: |
spherical averages, discrete, maximal functions, lacunary, Circle method. |
| Subject: |
Primary: 42B24, Secondary: 1105. |
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Abstract
We prove new lp(Zd) bounds for discrete spherical averages in dimensions d ≥ 5. We focus on the case of lacunary radii, first for general lacunary radii, and then for certain kinds of highly composite choices of radii. We follow a style of argument from our prior paper, addressing the full supremum. The relevant maximal operator is decomposed into several parts; each part requires only one endpoint estimate. |
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| Acknowledgements
Research supported in part by grant from the US National Science Foundation, DMS-1600693 and the Australian Research Council ARC DP160100153.
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| Author information
Robert Kesler:
School of Mathematics
Georgia Institute of Technology
Atlanta GA 30332, USA
robertmkesler@gmail.com
Michael T. Lacey:
School of Mathematics
Georgia Institute of Technology
Atlanta GA 30332, USA
lacey@math.gatech.edu
Darío Mena Arias:
CIMPA, Escuela de Matemática
Ciudad de la Investigacion, Universidad de Costa Rica
Sede Rodrigo Facio, San Pedro, Montes de Oca, San Jose 11501, Costa Rica
DARIO.MENAARIAS@ucr.ac.cr
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