On conditions for the weighted integrability of the sum of the series with monotonic coefficients with respect to the multiplicative systems
Коэффициенттерi монотонды мультипликативтiк жүйелер бойынша қатарлардың қосындысының салмақты интегралдану шарттары туралы
Об интегрируемости с весом суммы рядов с монотонными коэффициентами по мультипликативным системам
Turgumbaev M.Z. Suleimenova Z.R. Mukhambetzhan M.A.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 2197 - 210 pp.
In this paper, we studied the issues of integrability with the weight of the sum of series with respect to multiplicative systems, provided that the coefficients of the series are monotonic. The conditions for the weight function and the series’ coefficients are found; the sum of the series belongs to the weighted Lebesgue space Lp (1 < p < ∞). In addition, the case of p = 1 was considered. In this case, other conditions for the weighted integrability of the sum of the series under consideration are found. In the case of the generating sequence’s boundedness, the proved theorems imply an analogue of the well-known Hardy-Littlewood theorem on trigonometric series with monotone coefficients.
generator sequence , Hardy-Littlewood theorem , monotone coefficients , the multiplicative systems , the weighted integrability of the sum of series
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Karaganda Buketov University, 28 Universitetskaya street, Karaganda, 100028, Kazakhstan
Eurasian National University named after L.N.Gumilyov, 2 Satpayev street, Astana, 010008, Kazakhstan
Eurasian National University named after L.N.Gumilyov, 2 Satpayev street, Astana, 010008, Kazakhstan
Karaganda Buketov University
Eurasian National University named after L.N.Gumilyov
Eurasian National University named after L.N.Gumilyov
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