Strong convergence of two-dimensional Walsh-Fourier series

2014/10/05 by George Tephnadze · 1 citation
Mathematics · #math.CA #math.FA #msc:42C10

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published as Ukrainian Mathematical Journal (UMJ), 65, N6, (2013), 822-834 · Walsh system, Strong convergence, martingale Hardy space. arXiv admin note: text overlap with arXiv:1309.7548, arXiv:1310.8212 by other authors

arxiv created 2014/10/05 · arxiv updated 2014/10/28

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.

Citations

• Triangular Fejér Summability of Two-Dimensional Walsh-Fourier series
• Almost Everywhere Strong Summability of Double Walsh-Fourier Series

Cited by

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