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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 3, Pages 3–14
DOI: https://doi.org/10.26907/0021-3446-2024-3-3-14 (Mi ivm9959) 		 
Integrability of series with respect to multiplicative systems and generalized derivatives

N. Yu. Agafonova, S. S. Volosivets

Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia
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DOI: https://doi.org/10.26907/0021-3446-2024-3-3-14
Abstract: We give some necessary and sufficient conditions for the convergence of generalized derivatives of sums of series with respect to multiplicative systems and the corresponding Fourier series. These conditions are counterparts of trigonometric results of S. Sheng, W.O. Bray and $\check{C}$.V. Stanojević and extend some results of F. Móricz proved for Walsh–Fourier series.
Keywords: multiplicative system, $L^1$-integrability, $L^1$-convergence, generalized derivative.
Received: 02.02.2023
Revised: 02.02.2023
Accepted: 29.03.2023
Document Type: Article
UDC: 517.518
Language: Russian
Citation: N. Yu. Agafonova, S. S. Volosivets, “Integrability of series with respect to multiplicative systems and generalized derivatives”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 3, 3–14
Citation in format AMSBIB
\Bibitem{AgaVol24}
\by N.~Yu.~Agafonova, S.~S.~Volosivets
\paper Integrability of series with respect to multiplicative systems and generalized derivatives
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 3
\pages 3--14
\mathnet{http://mi.mathnet.ru/ivm9959}
\crossref{https://doi.org/10.26907/0021-3446-2024-3-3-14}
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