A weighted norm inequality for Vilenkin-Fourier series

Gosselin, John A.

doi:10.1090/S0002-9939-1975-0367547-3

A weighted norm inequality for Vilenkin-Fourier series
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by John A. Gosselin PDF

Proc. Amer. Math. Soc. 49 (1975), 349-353 Request permission

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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