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- W2071810993 abstract "S. V. Konyagin showed that if the one-dimensional Lebesgue constants for the Walsh-Paley system are unbounded, then the square partial sums of some integrable function diverge almost everywhere. On the other hand the author constructed an example of sequence for which, sup is finite, but for some integrable function the partial sums diverge almost everywhere. Thus boundedness of the Lebesgue constants is not a necessary and sufficient condition for the convergence almost everywhere of the partial sums of any integrable function. In this article we find such a necessary and sufficient condition." @default.
- W2071810993 created "2016-06-24" @default.
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- W2071810993 date "1995-08-31" @default.
- W2071810993 modified "2023-10-16" @default.
- W2071810993 title "A criterion for the almost-everywhere convergence of Fourier-Walsh square partial sums of integrable functions" @default.
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- W2071810993 doi "https://doi.org/10.1070/sm1995v186n07abeh000056" @default.
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