Multiplication properties and the Rellich-Kondrachov theorem in Herz-type Sobolev spaces

Douadi Drihem

Multiplication properties and the Rellich-Kondrachov theorem in Herz-type Sobolev spaces

Functional Analysis 2026-07-04 v1

Authors: Douadi Drihem

Abstract

In this paper, we prove that Herz-type Sobolev spaces form a Banach algebra and establish a Rellich--Kondrachov compactness theorem for these spaces. These results extend the corresponding classical theory and further demonstrate that Herz-type Sobolev spaces provide a natural generalization of the classical Sobolev spaces.

Keywords

Herz-type Sobolev spaces Banach algebra Rellich-Kondrachov theorem compactness function spaces

Cite

@article{arxiv.2607.03807,
  title  = {Multiplication properties and the Rellich-Kondrachov theorem in Herz-type Sobolev spaces},
  author = {Douadi Drihem},
  journal= {arXiv preprint arXiv:2607.03807},
  year   = {2026}
}