Convergence and divergence almost everywhere of spherical means for radial functions

Author:
Yūichi Kanjin

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1063-1069

MSC:
Primary 42B25

MathSciNet review:
954984

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Abstract: Let . It will be shown that the maximal operator of spherical means , is bounded on radial functions when , and it implies that, for every radial function converges to for a.e. when . Also, it will be proved that there is an radial function with compact support such that diverges for a.e. .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0954984-8

Keywords:
Maximal operator of spherical means for radial functions,
a.e. convergence,
a.e. divergence,
transplantation theorem,
Hankel transform

Article copyright:
© Copyright 1988
American Mathematical Society