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Displaying similar documents to “Martingale Hardy Spaces and Their Application in Fourier Analysis - F. Weisz.”

On the partial sums of Walsh-Fourier series

George Tephnadze (2015)

Colloquium Mathematicae

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We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.