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Matematicheskie Zametki, 2017, Volume 102, Issue 3, Pages 339–354
DOI: https://doi.org/10.4213/mzm11463 (Mi mzm11463) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Series in Multiplicative Systems in Lorentz Spaces

S. S. Volosivets

Saratov State University
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DOI: https://doi.org/10.4213/mzm11463
Abstract: Series in multiplicative systems $\chi$ with generalized monotone coefficients are studied. Necessary and sufficient Hardy–Littlewood type conditions for the sums of such series to belong to the Lorentz space are proved. As corollaries, we establish estimates of best approximation in the system $\chi$ and Konyushkov-type theorems on the equivalence of $O$- and $\asymp$-relations for the weighted sums of the Fourier coefficients in the system $\chi$ and for the best approximations.
Keywords: Lorentz space, multiplicative systems, best approximation, Konyushkov-type theorems on the equivalence of $O$- and $\asymp$-relations.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.1520.2014/K
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 1.1520.2014/K).
Received: 25.11.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 3, Pages 310–324
DOI: https://doi.org/10.1134/S0001434617090024
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: S. S. Volosivets, “Series in Multiplicative Systems in Lorentz Spaces”, Mat. Zametki, 102:3 (2017), 339–354; Math. Notes, 102:3 (2017), 310–324
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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