Abstract
In this paper, we introduce and we study Sobolev type spaces associated to Jacobi–Cherednik operator on
R
. Next we define the generalized Besov and Triebel spaces and study some of the properties. As applications on these spaces we establish the Sobolev embedding, the hypoellipticity for the Jacobi–Cherednik operator. We give some properties including some estimates for the solution of the generalized wave equation and the generalized Schrödinger equation. Also, some applications are given for these spaces.