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arXiv · 2303.01846

$(H_p-L_p)$ type inequalities for subsequences of N\"orlund means of Walsh-Fourier series

David Baramidze·Lars-Erik Persson·Kristoffer Tangrand·George Tephnadze
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Abstract

We investigate the subsequence $\{t_{2^n}f \}$ of N\"{o}rlund means with respect to the Walsh system generated by non-increasing and convex sequences. In particular, we prove that a big class of such summability methods are not bounded from the martingale Hardy spaces $H_p$ to the space $weak-L_p $ for $0<p<1/(1+\alpha) $, where $0<\alpha<1$. Moreover, some new related inequalities are derived. As application, some well-known and new results are pointed out for well-known summability methods, especially for N\"{o}rlund logarithmic means and Ces\`aro means.

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David Baramidze, Lars-Erik Persson, Kristoffer Tangrand, George Tephnadze. 2023-03-03. $(H_p-L_p)$ type inequalities for subsequences of N\"orlund means of Walsh-Fourier series. https://arxiv.org/abs/2303.01846

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