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Maximal operators associated to radial functions in $ L\sp{2}({\bf R}\sp{2})$

Author: N. E. Aguilera
Journal: Proc. Amer. Math. Soc. 80 (1980), 283-286
MSC: Primary 42B25; Secondary 44A15
MathSciNet review: 577760
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Abstract: Stein's result on spherical means imply that for $ n \geqslant 3$ the maximal operator associated to a radial function maps $ {L^p}({{\mathbf{R}}^n})$ boundedly into itself for $ p > n/(n - 1)$. In this paper we take a look at the case $ p = n = 2$.

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  • [1] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • [2] Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 0420116
  • [3] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110

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Article copyright: © Copyright 1980 American Mathematical Society

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