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

Abstract

We define and study Sobolev-type spaces WAs,pℝ+ associated with singular second-order differential operator on 0,∞. 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.