Description of the range of potentials, and hypersingular integrals

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)


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

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Number of pages44
Publication statusPublished - 2016
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Convolution operator
  • Fourier multiplier
  • Fractional derivative
  • Lizorkin space
  • Variable exponent

ASJC Scopus subject areas

  • Analysis


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