Strong convergence of two--dimensional Vilenkin-Fourier series

Abstract

We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space $H_p$ to the space $L_p$ for $0<p\le 1.$ We also prove that the sequence in the denominator cannot be improved.

References in corpus (1)

• A note on the strong convergence of two-dimensional Walsh-Fourier series