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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the Littlewood-Paley theory for mixed norm spaces
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by John A. Gosselin PDF
Trans. Amer. Math. Soc. 256 (1979), 113-124 Request permission

Abstract:

An inequality of Littlewood-Paley type is proved for the mixed norm spaces ${L_P}({l_r})$, $1 < p$, $r < \infty$, on the interval $[0,1]$. This result makes use of recent work by C. Fefferman and A. Cordoba on the boundedness of singular integrals on these spaces. As an application of this inequality, boundedness of the lacunary maximal partial sum operator for Walsh-Fourier series on ${L_p}({l_r})$ is established. This result can be viewed as an extension of a similar result for the Hardy-Littlewood maximal function due to C. Fefferman and E. M. Stein.
References
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 256 (1979), 113-124
  • MSC: Primary 42C10
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0546910-X
  • MathSciNet review: 546910