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This article is cited in 9 scientific papers (total in 9 papers)
$A$-integrable martingale sequences and Walsh series
V. A. Skvortsov M. V. Lomonosov Moscow State University
Abstract:
A sufficient condition for a Walsh series converging to an $A$-integrable function $f$ to be the $A$-Fourier's series of $f$ is stated in terms of uniform $A$-integrability of a martingale
subsequence of partial sums of the Walsh series. Moreover, the existence is proved of a Walsh series that converges almost everywhere to an $A$-integrable function and is not the
$A$-Fourier series of its sum.
Received: 25.05.2000
Citation:
V. A. Skvortsov, “$A$-integrable martingale sequences and Walsh series”, Izv. RAN. Ser. Mat., 65:3 (2001), 193–200; Izv. Math., 65:3 (2001), 607–615
Linking options:
https://www.mathnet.ru/eng/im342https://doi.org/10.1070/IM2001v065n03ABEH000342 https://www.mathnet.ru/eng/im/v65/i3/p193
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Abstract page: | 561 | Russian version PDF: | 218 | English version PDF: | 12 | References: | 72 | First page: | 3 |
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