Almost Everywhere Strong Summability of two-dimensional Walsh-Fourier Series
Ushangi Goginava
TL;DR
This paper proves that quadratic partial sums of two-dimensional Walsh-Fourier series are almost everywhere exponentially summable, using BMO-estimation techniques to establish strong convergence properties.
Contribution
It introduces a novel BMO-estimation approach to demonstrate almost everywhere exponential summability of quadratic partial sums in two-dimensional Walsh-Fourier series.
Findings
Quadratic partial sums are almost everywhere exponentially summable.
BMO-estimation is effective for analyzing Walsh-Fourier series.
The results improve understanding of convergence behavior in Walsh-Fourier analysis.
Abstract
It is proved a BMO-estimation for quadratic partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Approximation Theory and Sequence Spaces · Differential Equations and Boundary Problems