Some Aspects of Lw1r (G) boolean AND L(p, q, w(2)d mu) (G)

Abstract

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of L-w1(r) (G) boolean AND L(p, q, w(2)d mu) (G) spaces. Then the necessary conditions for compact embeddings of the spaces L-w1(r) (R-d) boolean AND L(p, q, w(2)d mu) (R-d) are showed.