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arXiv · 2605.05135

de la Vall\'ee Poussin Means of Walsh-Fourier Expansions

Ushangi Goginava
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Abstract

We study de la Vall\'ee Poussin means of Walsh--Fourier series associated with a nondecreasing window sequence. We establish a sharp criterion for almost everywhere convergence for integrable functions. We further show that, when this criterion fails, every Orlicz class below the logarithmic square-root scale contains a function whose de la Vall\'ee Poussin means diverge everywhere.

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Ushangi Goginava. 2026-05-06. de la Vall\'ee Poussin Means of Walsh-Fourier Expansions. https://arxiv.org/abs/2605.05135

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