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