Some Aspects of LRW1(G) ∩ L (P,q,w 2dμ)(G)

Abstract

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of Lr<inf>w1</inf>(G) ∩ L (p,q,w <inf>2</inf>dμ)(G) spaces. Then the necessary conditions for compact embeddings of the spaces Lr<inf>w1</inf> (R d ∩L(p,q,w <inf>2</inf>dμ)(R d ) are showed. © 2009 Editorial Office of CAM (Fudan University) and Springer-Verlag Berlin Heidelberg.