Gyrgy Gt, Ushangi Goginava

Uniform and L-convergence of Logarithmic Means of Double Walsh--Fourier Series

Abstract:
We discuss some convergence and divergence properties of two-dimensional (Nrlund) logarithmic means of two-dimensional Walsh-Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.

Keywords:
Double Walsh-Fourier series, logarithmic means, norm convergence.

MSC 2000: 42C10, 42B08