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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The weak behavior of spherical means
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by Carlos E. Kenig and Peter A. Tomas
Proc. Amer. Math. Soc. 78 (1980), 48-50
DOI: https://doi.org/10.1090/S0002-9939-1980-0548082-8

Abstract:

C. Fefferman has shown that the disc multiplier is not bounded on ${L^p}({{\mathbf {R}}^n}),n > 1,p \ne 2$. In contrast, C. Herz showed that, when restricted to ${L^p}$ radial functions, it is bounded on ${L^p}({{\mathbf {R}}^n})$ if and only if $2n/(n + 1) < p < 2n/(n - 1)$. We show that it is not weakly bounded for $p = 2n/(n + 1)$ or $p = 2n/(n - 1)$.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 48-50
  • MSC: Primary 42B15
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0548082-8
  • MathSciNet review: 548082