On the Almost Everywhere Convergence of Multiple Fourier-Haar Series

Abstract

The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set \(W\subset\mathbb{R}_+^n\) containing the intersection of some neighborhood of the origin with \(\mathbb{R}_+^n\). It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln⁺L)ⁿ⁻¹.