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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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  • 1. J. Bourgain, Estimations de certaines fonctions maximales, C. R. Acad. Sci. Paris 301, Série I (1985), 499-502. MR 87b:42023
  • 2. J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Anal. Math. 47 (1986), 69-85. MR 88f:42036
  • 3. A. Carbery, A. Seeger, S. Wainger and J. Wright, Classes of singular integral operators along variable lines, J. Geom. Anal. 9 (1999), 583-605. MR 2001g:42026
  • 4. A. Magyar, $L^p$-bounds for spherical maximal operators on $\mathbb{Z}^n$, Rev. Mat. Iberoamericana 13 (1997), 307-317. MR 99d:42031
  • 5. A. Magyar, E. M. Stein and S. Wainger, Discrete analogues in harmonic analysis: Spherical averages, Ann. of Math. 155 (2002), 189-208. MR 2003f:42028
  • 6. A. Seeger, T. Tao and J. Wright, Endpoint mapping properties of spherical maximal operators, J. Inst. Math. Jussieu 2 (2003), 109-144.
  • 7. E. M. Stein, Maximal functions I: Spherical means, Proc. Nat. Acad. Sci. 73 (1976), 2174-2175. MR 54:8133a

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Additional Information

Alexandru D. Ionescu
Affiliation: Department of Mathematics, University of Wisconsin at Madison, Madison, Wisconsin 53706

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

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