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Proceedings of the American Mathematical Society

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

 

 

A weighted norm inequality for Vilenkin-Fourier series


Author: John A. Gosselin
Journal: Proc. Amer. Math. Soc. 49 (1975), 349-353
MSC: Primary 42A56
DOI: https://doi.org/10.1090/S0002-9939-1975-0367547-3
MathSciNet review: 0367547
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Abstract: Various operators related to the Hardy-Littlewood maximal function have been shown to satisfy a strong type $ (p,p)$ condition, $ 1 < p < \infty $, for weighted $ {L^p}$ spaces providing the weight function satisfies the $ Ap$ condition of B. Muckenhoupt. In particular this result for the maximal partial sum operator for trigonometric series was established by R. Hunt and W. S. Young. In this note a result similar to that of Hunt and Young is established for Vilenkin-Fourier series, which include Walsh series as a special case.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0367547-3
Keywords: Weighted norm inequalities, maximal operators, joint distribution inequalities
Article copyright: © Copyright 1975 American Mathematical Society