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Two-weight Inequalities for Fractional Maximal Functions

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

Abstract

In this chapter necessary and sufficient conditions for boundedness of the fractional maximal functions \((\mathcal{M}_{\alpha(.)}f)(x) := \mathop{\rm{sup}}\limits_{{Q}\ni{x}} \frac{1}{\vert{Q}\vert^{1-\alpha(x)/{n}}} \int\limits_{Q} \vert{f}(y)\vert{dy}, \, \, \, 0 < \alpha_{-} \leqslant \alpha_{+} < {n}\), and Riesz potentials \((I^{\alpha(.)} {f})(x) := \int\limits_{\mathbb{R}^{n}} \frac{f(y)}{\vert{x - y}\vert^{n-\alpha(x)}}{dy}, \, \, \, 0 < \alpha_{-} \leqslant \alpha_{+} < {n}\) from L p (ℝ n , w) to L q (.)(ℝ n , v) are given in the case when the parameter α(.) and the weights are general-type functions.

Keywords

Maximal Function Lebesgue Space Fractional Integral Riesz Potential Doubling Condition 
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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