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Proceedings of the American Mathematical Society

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

 

 

A note on Walsh-Fourier series


Author: Wo Sang Young
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0410247-2
Article copyright: © Copyright 1976 American Mathematical Society