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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weak convergence of measures and weak type $(1,q)$ of maximal convolution operators
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by Filippo Chiarenza and Alfonso Villani PDF
Proc. Amer. Math. Soc. 97 (1986), 609-615 Request permission

Abstract:

Let ${G^ * }$ be the maximal convolution operator associated with a sequence of ${L^1}$ kernels. We show that if ${G^ * }$ is of weak type $(1,q)$, $1 \leq q < \infty$, over a subset ${\mathcal N}$ of ${\mathcal M}$ (the space of all finite positive Borel measures on ${{\bf {R}}^h}$ endowed with the weak topology), then ${G^ * }$ is of weak type $(1,q)$ over the closed cone in ${\mathcal M}$ generated by ${\mathcal N}$. As a particular case we obtain a well-known result by de Guzman.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 609-615
  • MSC: Primary 42B20; Secondary 28A33
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845974-2
  • MathSciNet review: 845974