Sobolev Type Spaces on the Dual of the Laguerre Hypergroup

Miloud Assal, M. Mounir Nessibi

Research output: Contribution to journalJournal articlepeer-review

12 Scopus citations

Abstract

Sobolev type spaces Eαs,p (α ≥ 0, s ∈ ℝ, p ∈ [1, +∞]) are defined on ℝ × ℕ by using the Fourier transform and its inverse on the Laguerre hypergroup. An analogue of Hs (ℝn), denoted by Hα s is investigated in this paper. Some properties including completeness and imbedding results for these spaces are given, Reillich-type theorem and Poincaré's inequality are proved. Also, global regularity results for certain differential operators are obtained.

Original languageEnglish
Pages (from-to)85-103
Number of pages19
JournalPotential Analysis
Volume20
Issue number1
DOIs
StatePublished - Feb 2004
Externally publishedYes

Keywords

  • Fourier Laguerre transfom
  • Peetre-type inequality
  • Poincaré's inequality
  • Regularity of solutions
  • Reillich-type theorem
  • Sobolev imbedding
  • Sobolev type spaces

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