Abstract
Sobolev type spaces E-alpha(s,p) (alpha greater than or equal to 0, s is an element of R, p is an element of [ 1,+infinity]) are defined on R x N by using the Fourier transform and its inverse on the Laguerre hypergroup. An analogue of H-s (R-n), denoted by Hs a is investigated in this paper. Some properties including completeness and imbedding results for these spaces are given, Reillich-type theorem and Poincare's inequality are proved. Also, global regularity results for certain differential operators are obtained.