Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. MR 0290095 (44:7280)
  • [2] -, Maximal functions: Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 2174-2175. MR 0420116 (54:8133a)
  • [3] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Univ. Press, New York, 1966. MR 1349110 (96i:33010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42B25, 44A15

Retrieve articles in all journals with MSC: 42B25, 44A15

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society