Integrability of the sum of absolute values of blocks of the Fourier-Walsh series for functions of bounded variation

被引：0
|
作者：
Yu. V. Malykhin
S. A. Telyakovskii
N. N. Kholshchevnikova
机构：
[1] Steklov Mathematical Institute of Russian Academy of Sciences,
[2] Moscow State University of Technology STANKIN,undefined
来源：
Proceedings of the Steklov Institute of Mathematics | 2015年 / 290卷
关键词：
Fourier Series; STEKLOV Institute; Bounded Variation; Lebesgue Constant; Walsh Function;
D O I：
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学科分类号：
摘要：
We establish necessary and sufficient conditions on a sequence that splits the Fourier–Walsh series into blocks under which the series consisting of the absolute values of such blocks of the Fourier–Walsh series of any function of bounded variation converges to an integrable function. We also obtain estimates for the L-norms of the Walsh–Dirichlet kernels and their differences.
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页码：306 / 317
页数：11
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