Weighted Lorentz-Karamata spaces and their compact embeddings

Abstract

Let G be a locally σ−compact abelian group with Haar measure. In this paper, firstly, weighted Lorentz-Karamata L w p,q;b (G) spaces will be defined and examined with some fundamental properties. Next, we will establish some criteria for noncompactness of embedding theorems for weighted Lorentz-Karamata (WLK) spaces.