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.
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).
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
\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}
Citation in format AMSBIB
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