Maximal operators associated to radial functions in $L^{2}(\textbf {R}^{2})$
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- by N. E. Aguilera PDF
- Proc. Amer. Math. Soc. 80 (1980), 283-286 Request permission
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 $p = n = 2$.References
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
- 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
Additional Information
- © Copyright 1980 American Mathematical Society
- 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