Strong convergence of two-dimensional Walsh-Fourier series
George Tephnadze
TL;DR
This paper proves that specific means of quadratical partial sums of two-dimensional Walsh-Fourier series are uniformly bounded operators from Hardy space to Lp space for 0<p<1, advancing understanding of Walsh-Fourier series convergence.
Contribution
It establishes uniform boundedness of certain means of two-dimensional Walsh-Fourier series from Hardy space to Lp space for the first time.
Findings
Boundedness of means in Hardy space for 0<p<1
Extension of Walsh-Fourier series convergence theory
New operator bounds for quadratical partial sums
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 to the space for
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