Sobolev type spaces on the dual of the Laguerre hypergroup (Q1424822)

In this paper the authors define the Sobolev type spaces \(E^{s,p}_\alpha\) (\(\alpha\geq 0\), \(s\in \mathbb R\), \(p\in [1,+\infty]\)) on \(\mathbb R\times \mathbb N\) by using the Fourier transform and its inverse on the Laguerre hypergroup. They give some properties including completeness and imbedding results for these spaces and prove a Rellich-type theorem and the Poincaré inequality. Next they obtain global regularity results for certain differential operators.