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arXiv · 1310.8212

Almost Everywhere Strong Summability of Double Walsh-Fourier Series

G. Gát·U. Goginava
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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 $(\frac{1}{n}\sum\limits_{m=0}^{n-1}\left\vert S_{mm}f - f \right\vert^{p})^{1/p}\rightarrow 0$ for every two-dimensional functions belonging to $L\log L$ and $0<p\le 2$. From the theorem of Getsadze \cite{Gets} it follows that the space $L\log L$ can not be enlarged with preserving this strong summability property.

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G. Gát, U. Goginava. 2013-10-30. Almost Everywhere Strong Summability of Double Walsh-Fourier Series. https://arxiv.org/abs/1310.8212

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