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 Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 323–334 (Mi tm3658)

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

Yu. V. Malykhina, S. A. Telyakovskiia, N. N. Kholshchevnikovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Moscow State Technological University "Stankin", Moscow, Russia

Abstract: 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.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 Russian Foundation for Basic Research 14-01-00417 The work of Yu.V. Malykhin and S.A. Telyakovskii (Sections 1, 2, and 4) is supported by the Russian Science Foundation under grant 14-50-00005 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. The work of N.N. Kholshchevnikova (Section 3) is supported by the Russian Foundation for Basic Research, project no. 14-01-00417.

DOI: https://doi.org/10.1134/S0371968515030279

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 306–317

Bibliographic databases:

UDC: 517.518.36

Citation: Yu. V. Malykhin, S. A. Telyakovskii, N. N. Kholshchevnikova, “Integrability of the sum of absolute values of blocks of the Fourier–Walsh series for functions of bounded variation”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 323–334; Proc. Steklov Inst. Math., 290:1 (2015), 306–317

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3658
• https://doi.org/10.1134/S0371968515030279
• http://mi.mathnet.ru/eng/tm/v290/p323

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This publication is cited in the following articles:
1. R. Toledo, “On the boundedness of the $L^1$-norm of Walsh-Fejér kernels”, J. Math. Anal. Appl., 457:1 (2018), 153–178
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