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Compactness criteria for fractional integral operators

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Published/Copyright: December 19, 2019
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 22 Issue 5

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

MSC 2010: Primary 26A33; Secondary 42B35; 47B38
Key Words and Phrases: fractional order integrals; quasi-metric spaces; compact operator

Acknowledgements

The second named author was supported by the National Science Centre of Poland project 2015/17/B/ST1/00064. The first and third authors were supported by the Shota Rustaveli National Science Foundation of Georgia (Project No. FR-18-2499).

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Received: 2019-03-01
Published Online: 2019-12-19
Published in Print: 2019-10-25

© 2019 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–Volume 22–5–2019)
  4. Survey Paper
  5. A survey on fractional asymptotic expansion method: A forgotten theory
  6. Simplified fractional-order design of a MIMO robust controller
  7. Research Paper
  8. Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
  9. Weyl integrals on weighted spaces
  10. On fractional regularity of distributions of functions in Gaussian random variables
  11. Compactness criteria for fractional integral operators
  12. Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
  13. Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
  14. Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
  15. Supercritical fractional Kirchhoff type problems
  16. Identification for control of suspended objects in non-Newtonian fluids
  17. Algebraic fractional order differentiator based on the pseudo-state space representation
  18. Eigenvalues for a combination between local and nonlocal p-Laplacians
https://doi.org/10.1515/fca-2019-0067
Keywords for this article
fractional order integrals; quasi-metric spaces; compact operator

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–Volume 22–5–2019)
  4. Survey Paper
  5. A survey on fractional asymptotic expansion method: A forgotten theory
  6. Simplified fractional-order design of a MIMO robust controller
  7. Research Paper
  8. Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets
  9. Weyl integrals on weighted spaces
  10. On fractional regularity of distributions of functions in Gaussian random variables
  11. Compactness criteria for fractional integral operators
  12. Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
  13. Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications
  14. Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation
  15. Supercritical fractional Kirchhoff type problems
  16. Identification for control of suspended objects in non-Newtonian fluids
  17. Algebraic fractional order differentiator based on the pseudo-state space representation
  18. Eigenvalues for a combination between local and nonlocal p-Laplacians
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