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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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Vector-valued inequalities for Fourier series
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by José L. Rubio De Francia PDF
Proc. Amer. Math. Soc. 78 (1980), 525-528 Request permission

Abstract:

Denoting by ${S^\ast }$ the maximal partial sum operator of Fourier series, we prove that ${S^\ast }({f_1},{f_2}, \ldots ,{f_k}, \ldots ) = ({S^\ast }{f_1},{S^\ast }{f_2}, \ldots ,{S^\ast }{f_k}, \ldots )$ is a bounded operator from ${L^p}({l^r})$ to itself, $1 < p,r < \infty$. Thus, we extend the theorem of Carleson and Hunt on pointwise convergence of Fourier series to the case of vector valued functions. We give also an application to the rectangular convergence of double Fourier series.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 525-528
  • MSC: Primary 42A20
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0556625-3
  • MathSciNet review: 556625