On weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems

dc.contributor.author	Turgumbaev, M.Zh.
dc.contributor.author	Suleimenova, Z.R.
dc.contributor.author	Tungushbaeva, D.I.
dc.date.accessioned	2024-12-18T07:42:21Z
dc.date.available	2024-12-18T07:42:21Z
dc.date.issued	2023
dc.identifier.issn	2663-5011
dc.identifier.other	DOI 10.31489/2023M2/160-168
dc.identifier.uri	http://rep.enu.kz/handle/enu/20328
dc.description.abstract	In this paper, we consider the questions about the weighted integrability of the sum of series with respect to multiplicative systems with monotone coefficients. Conditions are obtained for weight functions that ensure that the sum of such series belongs to the weighted Lebesgue space. The main theorems are proved without the condition that the generator sequence is bounded; in particular, it can be unbounded. In the case of boundedness of the generator sequence, the proved theorems imply an analogue of the well-known Hardy-Littlewood theorem on trigonometric series with monotone coefficients.	ru
dc.language.iso	en	ru
dc.publisher	Bulletin of the Karaganda University. Mathematics Series	ru
dc.subject	multiplicative systems	ru
dc.subject	decomposition	ru
dc.subject	weighted integrability	ru
dc.subject	sum of series	ru
dc.subject	generator sequence	ru
dc.subject	monotone coefficients	ru
dc.subject	Hardy-Littlewood theorem	ru
dc.subject	Lebesgue space	ru
dc.title	On weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems	ru
dc.type	Article	ru