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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, Volume 28, Number 4, Pages 78–90
DOI: https://doi.org/10.21538/0134-4889-2022-28-4-78-90 (Mi timm1952) 		 
Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation

S. S. Volosivets, A. N. Mingachev

Saratov State University
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DOI: https://doi.org/10.21538/0134-4889-2022-28-4-78-90
Abstract: The series of one-dimensional and two-dimensional Fourier coefficients with respect to multiplicative systems $\chi$ (with a bounded generating sequence ${\mathbf P}=\{p_i\}^\infty_{i=1}$) with weights satisfying Gogoladze–Meskhia type conditions are studied. Sufficient conditions for the convergence of such series are established for functions from different classes of generalized bounded fluctuation.
Keywords: absolute convergence, multiplicative system, double series, generalized bounded fluctuation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006
The research of the first author was supported by the Ministry of Science and Higher Education of the Russian Federation within the State Assignment (agreement no. FSRR-2020-0006).
Received: 23.07.2022
Revised: 21.10.2022
Accepted: 31.10.2022
Bibliographic databases:
Document Type: Article
UDC: 517.518.36
MSC: 42C10
Language: Russian
Citation: S. S. Volosivets, A. N. Mingachev, “Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 4, 2022, 78–90
Citation in format AMSBIB
\Bibitem{VolMin22}
\by S.~S.~Volosivets, A.~N.~Mingachev
\paper Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2022
\vol 28
\issue 4
\pages 78--90
\mathnet{http://mi.mathnet.ru/timm1952}
\crossref{https://doi.org/10.21538/0134-4889-2022-28-4-78-90}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531177}
\elib{https://elibrary.ru/item.asp?id=49866449}
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