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Matematicheskie Zametki, 2020, Volume 107, Issue 2, Pages 195–209
DOI: https://doi.org/10.4213/mzm11965 (Mi mzm11965) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Generalized Absolute Convergence of Single and Double Series in Multiplicative Systems

S. S. Volosivets, M. A. Kuznetsova

Saratov State University
Full-text PDF (546 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm11965
Abstract: Series of one- and two-dimensional Fourier coefficients in multiplicative systems $\chi$ (with 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 for continuous (in a generalized sense) functions and functions from ${\mathbf P}$-ary Hardy space are established. The question of whether these conditions are unimprovable is investigated. Sufficient conditions for generalized absolute convergence for functions of bounded $(\Lambda,\Psi)$-fluctuation are also established.
Keywords: multiplicative system, Gogoladze–Meskhia-type conditions, generalized absolute convergence, $\mathbf P$-ary Hardy space.
Received: 13.02.2018
Revised: 20.07.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 2, Pages 217–230
DOI: https://doi.org/10.1134/S0001434620010216
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: S. S. Volosivets, M. A. Kuznetsova, “Generalized Absolute Convergence of Single and Double Series in Multiplicative Systems”, Mat. Zametki, 107:2 (2020), 195–209; Math. Notes, 107:2 (2020), 217–230
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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