Almost Everywhere Strong Summability of Double Walsh-Fourier Series

2013/10/30 by Gát, G., Goginava, U.
#42C10 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.8212

Abstract

In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation ((1)/(n)∑_m=0^n-1\vert S_mmf - f \vert^p)^1/p→ 0 for every two-dimensional functions belonging to Llog L and 0

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