On a subalgebra of L1w(G)

Let G be a locally compact abelian group with Haar measure. We define the spaces B1,w(p,q) =L1w(G)?(Lp,`q)(G) and discuss some properties of these spaces. We show that B1,w(p,q) is an Sw(G) space. Furthermore we investigate compact embeddings and the multipliers of B1,w(p,q).