Cherednik-Sobolev spaces and applications

Abstract

In this paper we introduce and we study the Sobolev type spaces associated to Cherednik operators on \({\mathbb{R }}^{d}\). Next we define the generalized Besov and Triebel spaces and we study some of properties. As applications on these spaces we establish the Sobolev embedding, the hypoellipticity for the Cherednik operators. We give some properties including some estimates for the solution of the generalized wave equation and the generalized Schrodinger equation. Also, some applications are given for these spaces.