Compactness Criteria for Fractional Integral Operators

被引：0
|
作者：
Vakhtang Kokilashvili
Mieczysław Mastyło
Alexander Meskhi
机构：
[1] I. Javakhishvili Tbilisi State University,Department of Mathematical Analysis A. Razmadze Mathematical Institute
[2] Adam Mickiewicz University,Faculty of Mathematics and Computer Science
[3] Poznań,Department of Mathematics Faculty of Informatics and Control Systems
[4] Georgian Technical University,undefined
来源：
Fractional Calculus and Applied Analysis | 2019年 / 22卷
关键词：
Primary 26A33; Secondary 42B35; 47B38; fractional order integrals; quasi-metric spaces; compact operator;
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学科分类号：
摘要：
We establish necessary and sufficient conditions for the compactness of fractional integral operators from Lp}(X, μ) to Lq(X, μ) with 1 < p < q < ∞, where μ is a measure on a quasi-metric measure space X. As an application we obtain criteria for the compactness of fractional integral operators defined in weighted Lebesgue spaces over bounded domains of the Euclidean space ℝn with the Lebesgue measure, and also for the fractional integral operator associated to rectifiable curves of the complex plane.
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页码：1269 / 1283
页数：14
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