On weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems
Коэффициенттерi монотонды мультипликативтiк жүйелер бойынша қатарлардың қосындысының салмақты интегралдануы туралы
Об интегрируемости с весом суммы рядов с монотонными коэффициентами по мультипликативным системам
Turgumbaev M.Zh. Suleimenova Z.R. Tungushbaeva D.I.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 2160 - 168 pp.
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. All rights reserved
decomposition , generator sequence , Hardy-Littlewood theorem , Lebesgue space , monotone coefficients , multiplicative systems , sum of series , weighted integrability
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Karaganda University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
L.N. Gumilyov Eurasian national university, Astana, Kazakhstan
Karaganda University of the name of academician E.A. Buketov
L.N. Gumilyov Eurasian national university
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