On Λ-Convergence Almost Everywhere of Multiple Trigonometric Fourier Series

Abstract

We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the λ-convergence for λ>1. The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class L(ln+L)dln+ln+ln+L([0,2π)d) has been generalized to the case of the Λ-convergence for some sequences Λ.