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

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On double cosine, sine, and Walsh series with monotone coefficients
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by Ferenc Móricz PDF
Proc. Amer. Math. Soc. 109 (1990), 417-425 Request permission

Abstract:

We extend from one-dimensional to two-dimensional series the results by Hardy and Littlewood [6] on the ${L^r}$-integrability of the sum $f$ and the results by Stechkin [10] on the ${L^1}$-integrability of the maximum partial sum ${M^*}$ in the case of cosine and sine series with monotone coefficients. Among others, we prove that the ${L^r}$-integrability of $f$ and ${M^*}$ is essentially equivalent for $r > 1$ in the two-dimensional setting, too. Simultaneously, we extend our earlier results in [7] from one-dimensional to two-dimensional Walsh series.
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 109 (1990), 417-425
  • MSC: Primary 42B05; Secondary 42A32
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1010803-4
  • MathSciNet review: 1010803