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⊂R+n containing the intersection of some neighborhood of the origin with 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.