Embedding theorems for Herz-Type Sobolev spaces on domains

Abstract

In this paper, we further investigate the properties of Herz-type Sobolev spaces on domains, which unify and generalize the classical Sobolev spaces. In particular, we establish several Sobolev-type embedding theorems for these spaces. Moreover, by means of a suitable example, we show that some of the assumptions imposed on the parameters are optimal.