Advertisement

Kernel Integral Operators

  • Vakhtang Kokilashvili
  • Alexander Meskhi
  • Humberto Rafeiro
  • Stefan Samko
Chapter
  • 535 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 248)

Abstract

This chapter is devoted mainly to the study of the boundedness/compactness of the weighted Volterra integral operators \({K}_{v} {f}(x) = v(x) \int\limits_{0}^{x} k(x, t)f(t)dt, \, \, \, \, x > 0,\) and \(\mathcal({K}_{v}{f})(x) = {v}(x) \int\limits_{-\infty}^{x} {k}(x, t){f}(t){dt}, \, \, \, {x} \in \mathbb{R} \), in variable exponent Lebesgue spaces and variable exponent amalgam spaces (VEAS) under the log-condition on exponents of spaces, where v is an a.e. positive function.

Keywords

Maximal Function Liouville Operator Variable Exponent Banach Function Space Kernel Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 1
  • Humberto Rafeiro
    • 2
  • Stefan Samko
    • 3
  1. 1.A. Razmadze Mathematical InstituteI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Departam ento de MatemáticasPontificia Universidad JaverianaBogotáColombia
  3. 3.Faculdade de Ciências e TecnologiaUniversidade do AlgarveFaroPortugal

Personalised recommendations