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Positivity

, Volume 17, Issue 4, pp 1123–1140 | Cite as

Positive kernel operators in \(L^{p(x)}\) spaces

  • Vakhtang Kokilashvili
  • Alexander Meskhi
  • Muhammad Asad ZaighumEmail author
Article
  • 189 Downloads

Abstract

A characterization of a weight \(v\) governing the boundedness/compactness of the weighted kernel operator \(K_v\) in variable exponent Lebesgue spaces \(L^{p(\cdot )}\) is established under the log-Hölder continuity condition on exponents of spaces. The kernel operator involves, for example, weighted variable parameter fractional integral operators. The distance between \(K_v\) and the class of compact integral operators acting from \(L^{p(\cdot )}\) to \(L^{q(\cdot )}\) (measure of non-compactness) is also estimated from above and below.

Keywords

Variable exponent Lebesgue spaces Positive kernel operator Boundedness Compactness Measure of non-compactness 

Mathematics Subject Classification (2000)

46E30 47B34 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Vakhtang Kokilashvili
    • 1
    • 2
  • Alexander Meskhi
    • 1
    • 3
  • Muhammad Asad Zaighum
    • 4
    Email author
  1. 1.Department of Mathematical Analysis, A. Razmadze Mathematical InstituteI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.International Black Sea UniversityTbilisiGeorgia
  3. 3.Department of MathematicsFaculty of Informatics and Control Systems, Georgian Technical UniversityTbilisiGeorgia
  4. 4.Abdus Salam School of Mathematical SciencesGC University68-B New Muslim TownPakistan

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