WEIGHTED INEQUALITIES FOR A SUPERPOSITION OF THE THREE OPERATORS

ҮШ ОПЕРАТОРДЫҢ СУПЕРПОЗИЦИЯСЫ ҮШІН САЛМАҚТЫ ТЕҢСІЗДІКТЕР
ВЕСОВЫЕ НЕРАВЕНСТВА ДЛЯ СУПЕРПОЗИЦИИ ТРЕХ ОПЕРАТОРОВ
Abek A.N. Gogatishvili A. Bokayev N.A. Ünver T.
2025 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2025 #22 Issue 4 295 - 305 pp.

We study a three-weight inequality for a superposition of the Copson, Hardy, and Tandori operators. The goal of this paper is to prove a complete characterization of the boundedness of the operator that is a combination of these three operators in weighted Lebesgue spaces from to. The main focus is on determining necessary and sufficient conditions under which this inequality holds for all non-negative measurable functions on the positive real axis. The notion of a fundamental function of a Borel measure with respect to an increasing function is used substantially. Since the Tandori operator is not a linear operator, we cannot use the duality methods used in earlier works. To solve this problem, we develop a new, simplified discretization method that avoids the complexities of previously known methods. An explicit form of the best constant in the inequality is obtained, demonstrating the accuracy and optimality of the results. By establishing necessary and sufficient conditions for the boundedness of these composite operators, we improve the inequalities previously established in the works of Gogatishvili A., Pick L., Opic B. [1]. The results obtained in the paper extend and complement existing research in the field of weighted inequalities and operator analysis in function spaces and offer potential applications in approximation theory, harmonic analysis and related areas.

best constant , Copson operator , discretization , Hardy operator , superposition of operators , supremal operator , Tandori operator , weighted inequality

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L.N. Gumilyov Eurasian national university, Astana, Kazakhstan
Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic
Kirikkale University, Kirikkale, Turkey

L.N. Gumilyov Eurasian national university
Institute of Mathematics of the Czech Academy of Sciences
Kirikkale University

10 лет помогаем публиковать статьи Международный издатель

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