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This article is cited in 17 scientific papers (total in 18 papers)
Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems
S. V. Bochkarev Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
In this paper a new construction of everywhere divergent Fourier–Walsh series is presented. This construction enables one to halve the gap in the Lebesgue–Orlicz classes between the Schipp–Moon lower bound established by using Kolmogorov's construction and the Sjölin
upper bound obtained by using Carleson's method. Fourier series which are everywhere divergent after a rearrangement are constructed with respect to the Walsh system (and to more general systems of characters) with the best lower bound for the Weyl factor. Some results
related to an upper bound of the majorant for partial sums of series with respect to rearranged
multiplicative systems are established. The results thus obtained show certain merits of harmonic analysis on the dyadic group in clarifying and overcoming fundamental difficulties in the solution of the main problems of Fourier analysis.
Received: 20.11.2003
Citation:
S. V. Bochkarev, “Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems”, Uspekhi Mat. Nauk, 59:1(355) (2004), 103–124; Russian Math. Surveys, 59:1 (2004), 103–124
Linking options:
https://www.mathnet.ru/eng/rm703https://doi.org/10.1070/RM2004v059n01ABEH000703 https://www.mathnet.ru/eng/rm/v59/i1/p103
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Abstract page: | 781 | Russian version PDF: | 335 | English version PDF: | 22 | References: | 84 | First page: | 3 |
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