S.S. Volosivets, A.N. Mingachev. Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation ... P. 78-90

The series of one-dimensional and two-dimensional Fourier coefficients with respect to multiplicative systems $\chi$ (with a bounded generating sequence ${\bf P}=\{p_i\}^\infty_{i=1}$) 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

Received July 26, 2022

Revised October 21, 2022

Accepted October 31, 2022

Funding Agency: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).

Sergey Sergeevich Volosivets, Cand. Sci. (Phys.-Math.), Saratov State University, Saratov, 410012 Russia, e-mail: volosivetsss@mail.ru

Alexandr Nikolaevich Mingachev, student, Saratov State University, Saratov, 410012 Russia, e-mail: sashamin2011@yandex.ru

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Cite this article as: S.S. Volosivets, A.N. Mingachev. Generalized absolute convergence of Fourier series with respect to multiplicative systems of functions of generalized bounded fluctuation. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 4, pp. 78–90.