Almost Everywhere Strong Summability of Fejer means of rectangular partial sums of two-dimensional Walsh-Fourier Series

TL;DR

This paper establishes that rectangular partial sums of two-dimensional Walsh-Fourier series are almost everywhere exponentially summable, supported by a BMO-estimation, advancing the understanding of Walsh-Fourier series convergence.

Contribution

It introduces a BMO-estimation approach to prove almost everywhere exponential summability of rectangular partial sums in two-dimensional Walsh-Fourier series.

Findings

BMO-estimation for rectangular partial sums

Almost everywhere exponential summability proven

Advances convergence theory of Walsh-Fourier series

Abstract

It is proved a BMO-estimation for rectangular partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of rectangular partial sums of double Walsh-Fourier series.