Strong convergence of two-dimensional Walsh-Fourier series

Abstract

We prove that certain mean of the quadratical partial sums of the two-dimensional Walsh-Fourier series are uniformly bounded operators from the Hardy space $H_p$ to the space $L_p$ for $0<p<1.$

arXiv commentWalsh system, Strong convergence, martingale Hardy space. arXiv admin note: text overlap with arXiv:1309.7548, arXiv:1310.8212 by other authors