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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0577760-X
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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  • [2] Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 0420116
    Elias M. Stein, Maximal functions. II. Homogeneous curves, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2176–2177. MR 0420117
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577760-X
Article copyright: © Copyright 1980 American Mathematical Society