Dunkl-Sobolev spaces of exponential type and applications (Q646797)

The Silva space is considered in this paper, and then the Dunkl transform is proved to be an isomorphism from the Silva space onto itself. Further, the result, so obtained, is extended to the dual of the Silva space. By introducing the generalized Dunkl-Sobolev space of exponential type, involving an exponential weight function and the Lebesgue spaces associated with the Dunkl transform, the author investigates imbedding theorems and structure theorems. Two applications on the Dunkl--Sobolev spaces of exponential type are also given.