György Gát, Ushangi Goginava, George Tkebuchava

Convergence in Measure of Logarithmic Means of Double Walsh-Fourier Series

Abstract:
The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of $L\log L(I^{2})$, the set of functions for which quadratic logarithmic means of the double Walsh-Fourier series converge in measure is of first Baire category.

Keywords:
Double Walsh-Fourier series, Orlicz space, convergence in measure.

MSC 2000: 42C10