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arXiv · 2201.08493

Some new results for subsequences of N\"orlund logarithmic means of Walsh-Fourier series

D. Baramidze·L. -E. Persson·H. Singh·G. Tephnadze
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Abstract

We prove that there exists a martingale $f\in H_p $ such that the subsequence $\{L_{2^n}f \}$ of N\"orlund logarithmic means with respect to the Walsh system are not bounded in the Lebesgue space $weak-L_p $ for $0<p<1 $. Moreover, we prove that for any $f\in L_p(G),$ $p\geq 1, $ $L_{2^n}f$ converge to $f$ at any Lebesgue point $x$. Some new related inequalities are derived.

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D. Baramidze, L. -E. Persson, H. Singh, G. Tephnadze. 2022-01-21. Some new results for subsequences of N\"orlund logarithmic means of Walsh-Fourier series. https://arxiv.org/abs/2201.08493

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