Sobolev type spaces on the dual of the Laguerre hypergroup
type: Item
instance of: scholarly article
title: Sobolev type spaces on the dual of the Laguerre hypergroup
zbMATH Open document ID: 1060.42010
DOI: 10.1023/A:1025542009772
author: Miloud Assal
author: M. Mounir Nessibi
published in: Potential Analysis
publication date: 2004-03-15T00:00:00Z
review text: In this paper the authors define the Sobolev type spaces \(E^{s,p}_\alpha\) (\(\alpha\geq 0\), \(s\in \mathbb R\), \(p\in [1,+\infty]\)) on \(\mathbb R\times \mathbb N\) by using the Fourier transform and its inverse on the Laguerre hypergroup. They give some properties including completeness and imbedding results for these spaces and prove a Rellich-type theorem and the Poincaré inequality. Next they obtain global regularity results for certain differential operators.
reviewed by: Khalifa Trimèche
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 2057495
zbMATH Keywords: Sobolev type spaces
zbMATH Keywords: Fourier-Laguerre transform
zbMATH Keywords: Peetre-type inequality
zbMATH Keywords: Rellich-type theorem
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: Sobolev imbedding
zbMATH Keywords: regularity of solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2057495