Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces-Reference-Cited by-同舟云学术

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

Published:2020-10-01 Issue:5 Volume:23 Page:1452-1471
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Kokilashvili Vakhtang¹,Meskhi Alexander¹²

Affiliation:

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

2. Kutaisi International University Youth Avenue , Turn 5/7, 4600 , Kutaisi , Georgia

Abstract

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0072/pdf

Reference25 articles.

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4. C. Capone, A. Fiorenza, On small Lebesgue spaces. J. Funct. Spaces Appl. 3 (2005), 73–89.

5. D.E. Edmunds, V. Kokilashvili, A. Meskhi, Bounded and Compact Integral Operators. Kluwer Academic Publishers, Dordrecht (2002).

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