Published May 2021
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Dimension-Free L^p-Maximal Inequalities for Spherical Means in ℤ^N_(m+1)
Abstract
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.
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 (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received: 29 November 2017; Revision received: 17 July 2018; Accepted: 01 October 2018; Published: 27 February 2019.Attached Files
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Additional details
- Alternative title
- Dimension-Free Lp-Maximal Inequalities for Spherical Means in ℤNm+1
- Eprint ID
- 111127
- Resolver ID
- CaltechAUTHORS:20210930-194531157
- Created
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2021-10-04Created from EPrint's datestamp field
- Updated
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2021-10-04Created from EPrint's last_modified field