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Description of the Range of Potentials, and Hypersingular Integrals

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

Abstract

In this chapter we give a complete characterization of the range I α [L p (.)(ℝ n )] in terms of the convergence of hypersingular integrals of order α. The proof is based, in particular, on the results on denseness in L p (.)(ℝ n ) of Schwartz functions orthogonal to polynomials, and the inversion of the Riesz potential operator by means of hypersingular integrals.

Keywords

Fractional Derivative Convolution Operator Fourier Multiplier Variable Exponent Lizorkin Space 
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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