## Abstract and Applied Analysis

### Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications

#### Abstract

We define and study Sobolev-type spaces ${W}_{A}^{s,p}({\Bbb R}_{+})$ associated with singular second-order differential operator on $(0,\infty )$. Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 248725, 13 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606525

Digital Object Identifier
doi:10.1155/2014/248725

Mathematical Reviews number (MathSciNet)
MR3178858

Zentralblatt MATH identifier
07021994

#### Citation

Jelassi, Mourad; Mejjaoli, Hatem. Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 248725, 13 pages. doi:10.1155/2014/248725. https://projecteuclid.org/euclid.aaa/1412606525

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