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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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A note on Walsh-Fourier series
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by Wo Sang Young PDF
Proc. Amer. Math. Soc. 59 (1976), 305-310 Request permission

Abstract:

It is shown that the double sequence $\{ {\lambda _{mn}}\}$ with ${\lambda _{mn}} = 1$ if $n \leqslant m$ and $0$ otherwise is an ${L^p}$ multiplier for the Walsh system in two dimensions only if $p = 2$. This result is then used to show that the one-dimensional trigonometric system and the Walsh system are nonequivalent bases of the Banach space ${L^p}[0,\;1]$, and hence have different ${L^p}$ multipliers, $1 < p < \infty ,\;p \ne 2$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 305-310
  • MSC: Primary 42A56
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0410247-2
  • MathSciNet review: 0410247