Sobolev spaces in the generalized distribution spaces of Beurling type (Q1192566)

The authors define the concept of the generalized distribution spaces of Beurling type \(H^ s_ \omega\) as an extension of the classical Sobolev spaces. They study its basic properties -- completeness, density, duality -- and they formulate the Sobolev imbedding theorem and Rellich compactness theorem for these generalized Sobolev spaces.