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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An endpoint estimate for the discrete spherical maximal function


Author: Alexandru D. Ionescu
Journal: Proc. Amer. Math. Soc. 132 (2004), 1411-1417
MSC (2000): Primary 42B25
Published electronically: August 20, 2003
MathSciNet review: 2053347
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Abstract: We prove that the discrete spherical maximal function extends to a bounded operator from $L^{d/(d-2),1}(\mathbb{Z}^d)$ to $L^{d/(d-2),\infty}(\mathbb{Z}^d)$ in dimensions $d\geq 5$. This is an endpoint estimate for a recent theorem of Magyar, Stein and Wainger.


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Additional Information

Alexandru D. Ionescu
Affiliation: Department of Mathematics, University of Wisconsin at Madison, Madison, Wisconsin 53706
Email: ionescu@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07207-1
PII: S 0002-9939(03)07207-1
Received by editor(s): November 11, 2002
Received by editor(s) in revised form: December 31, 2002
Published electronically: August 20, 2003
Additional Notes: The author was supported in part by the National Science Foundation under NSF Grant No. 0100021
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society