Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup

Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Under the standard assumptions on the variable exponent p (x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space Bα [Lp (ṡ) (Rn)] in terms of the rate of convergence of the Poisson semigroup Pt. We show that the existence of the Riesz fractional derivative Dα f in the space Lp (ṡ) (Rn) is equivalent to the existence of the limit frac(1, εα) (I - Pε)α f. In the pre-limiting case supx p (x) < frac(n, α) we show that the Bessel potential space is characterized by the condition {norm of matrix} (I - Pε)α f {norm of matrix}p (ṡ) ≦ C εα.

Original languageEnglish
Pages (from-to)483-497
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume365
Issue number2
DOIs
Publication statusPublished - May 15 2010
Externally publishedYes

Keywords

  • Bessel potential space
  • Grünwald-Letnikov approach
  • Hypersingular integral
  • Riesz fractional derivative
  • Riesz potential operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup'. Together they form a unique fingerprint.

Cite this