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Hardy-type Operators in Variable Exponent Lebesgue Spaces

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

Abstract

In this chapter we consider the Hardy-type operators \({H}^{\alpha,\mu} f(x) = {x}^{\alpha(x)+\mu(x)-1} \int\limits_{0}^{x} \frac{{f}(y) {dy}} {y^{\alpha(y)}}, \, \, \mathcal{H}_{\beta,\mu}f(x) = {x}^{\beta(x)+\mu(x)} \int\limits_{x}^{\infty} \frac{{f}(y) {dy}}{y^{\beta(y)+1}},\) with variable exponents, in variable exponent Lebesgue spaces.

Keywords

Convolution Operator Decay Condition Hardy Inequality Variable Exponent Hardy 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.

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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

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