The discrete spherical maximal function: A new proof of $\ell ^2$-boundedness
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- by Neil Lyall, Ákos Magyar, Alex Newman and Peter Woolfitt
- Proc. Amer. Math. Soc. 149 (2021), 5305-5312
- DOI: https://doi.org/10.1090/proc/15639
- Published electronically: September 21, 2021
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Abstract:
We provide a new direct proof of the $\ell ^2$-boundedness of the Discrete Spherical Maximal Function that neither relies on abstract transference theorems (and hence Stein’s Spherical Maximal Function Theorem) nor on delicate asymptotics for the Fourier transform of discrete spheres.References
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Bibliographic Information
- Neil Lyall
- Affiliation: Department of Mathematics, The University of Georgia, Athens, Georgia 30602
- MR Author ID: 813614
- Email: lyall@math.uga.edu
- Ákos Magyar
- Affiliation: Department of Mathematics, The University of Georgia, Athens, Georgia 30602
- Email: magyar@math.uga.edu
- Alex Newman
- Affiliation: Department of Mathematics, The University of Georgia, Athens, Georgia 30602
- ORCID: 0000-0002-3795-7100
- Email: alxjames@uga.edu
- Peter Woolfitt
- Affiliation: Department of Mathematics, The University of Georgia, Athens, Georgia 30602
- Email: pwoolfitt@uga.edu
- Received by editor(s): September 7, 2020
- Received by editor(s) in revised form: April 6, 2021
- Published electronically: September 21, 2021
- Additional Notes: The first and second authors were partially supported by grants NSF-DMS 1702411 and NSF-DMS 1600840, respectively
- Communicated by: Dmitriy Bilyk
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 5305-5312
- MSC (2020): Primary 42B25
- DOI: https://doi.org/10.1090/proc/15639
- MathSciNet review: 4327433