Compactness criteria for fractional integral operators-Reference-Cited by-同舟云学术

Compactness criteria for fractional integral operators

Published:2019-10-01 Issue:5 Volume:22 Page:1269-1283
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Kokilashvili Vakhtang¹,Mastyło Mieczysław²,Meskhi Alexander³

Affiliation:

1. Department of Mathematical Analysis A. Razmadze Mathematical Institute , I. Javakhishvili Tbilisi State University , 6. Tamarashvili St., 0177 , Tbilisi , Georgia

2. Faculty of Mathematics and Computer Science , Adam Mickiewicz University, Poznań , Uniwersytetu Poznańskiego 4 61-614 , Poznań , Poland

3. Department of Mathematics Faculty of Informatics and Control Systems , Georgian Technical University , 77, Kostava St ., Tbilisi , Georgia

Abstract

Abstract 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 ℝ n with the Lebesgue measure, and also for the fractional integral operator associated to rectifiable curves of the complex plane.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2019-0067/pdf

Reference19 articles.

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