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A weighted norm inequality for Vilenkin-Fourier series

Author: John A. Gosselin
Journal: Proc. Amer. Math. Soc. 49 (1975), 349-353
MSC: Primary 42A56
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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Keywords: Weighted norm inequalities, maximal operators, joint distribution inequalities
Article copyright: © Copyright 1975 American Mathematical Society

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