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Dimension-Free L^p-Maximal Inequalities for Spherical Means in ℤ^N_(m+1)

Greenblatt, Jordan and Kolla, Alexandra and Krause, Ben (2021) Dimension-Free L^p-Maximal Inequalities for Spherical Means in ℤ^N_(m+1). International Mathematics Research Notices, 2021 (9). pp. 6586-6620. ISSN 1073-7928. doi:10.1093/imrn/rnz013.

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We extend the main result of Krause—the existence of dimension-free L^p-bounds, p>1⁠, for the spherical maximal function in the hypercube, {0,1}^N—to all cyclic groups, Z^N_(m+1), m≥1⁠. Our approach follows that of Krause, which grew out of the arguments of Harrow, Kolla, and Schulman, which were in turn motivated by the spectral technique developed by Nevo and Stein, and by Stein, in the context of pointwise ergodic theorems on general groups.

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Alternate Title:Dimension-Free Lp-Maximal Inequalities for Spherical Means in ℤNm+1
Additional Information:© The Author(s) 2019. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Received: 29 November 2017; Revision received: 17 July 2018; Accepted: 01 October 2018; Published: 27 February 2019.
Issue or Number:9
Record Number:CaltechAUTHORS:20210930-194531157
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Official Citation:Jordan Greenblatt, Alexandra Kolla, Ben Krause, Dimension-Free Lp-Maximal Inequalities for Spherical Means in ℤm+1N, International Mathematics Research Notices, Volume 2021, Issue 9, May 2021, Pages 6586–6620,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111127
Deposited By: Tony Diaz
Deposited On:04 Oct 2021 20:33
Last Modified:04 Oct 2021 20:35

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