WEIGHT INEQUALITIES FOR THE SUM OF SERIES WITH RESPECT TO THE MULTIPLICATIVE SYSTEMS
МУЛЬТИПЛИКАТИВТІК ЖҮЙЕЛЕР БОЙЫНША ҚАТАРЛАРДЫҢ ҚОСЫНДЫСЫНА АРНАЛҒАН САЛМАҚТЫ ТЕҢСІЗДІКТЕР
ВЕСОВЫЕ НЕРАВЕНСТВА ДЛЯ СУММЫ РЯДОВ ПО МУЛЬТИПЛИКАТИВНЫМ СИСТЕМАМ
Turgumbaev M.Z. Mukhambetzhan M.A. Suleimenova Z.R.
2025Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2025#22Issue 3231 - 242 pp.
This paper investigates series over Price multiplicative systems with coefficients belonging to the class of sequences of bounded variation. Conditions are obtained for estimating the norm of the sum of such series in weighted Lebesgue spaces. These conditions are formulated in terms of the weight function and the corresponding weight sequence. The methodology relies on techniques of harmonic analysis, the Abel transformation, and the Muckenhoupt criteria for the boundedness of the Hardy operator in weighted Lebesgue spaces. Additionally, discrete three-weight Hardy inequalities are considered, and their applicability to the analyzed series is examined. The main theorems establish a relationship between the variation of the coefficients and the integral characteristics of the weights. The results extend the applicability of known analytical methods to a wider class of functional series and are of interest in harmonic analysis, series theory, and the estimation of solutions to differential equations in functional spaces.
Hardy operator , integrability conditions , multiplicative systems , sequence from the class of bounded variation , weighted Lebesgue spaces
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Karaganda Buketov University, Karaganda, Kazakhstan
Eurasian National University, Astana, Kazakhstan
Karaganda Buketov University
Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026