Multipliers and tensor products of weighted Lp-spaces

Abstract

Let G be a locally compact unimodular group with Haar measure rmdx and ? be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Ap,q? (G) and prove that Ap,q? (G) is a translation invariant Banach space. Furthermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Ap,q? (G) admits an approximate identity bounded in L1?. (G). It is also proved that the space Lp? (G) ?L1? L?q? (G) is isometrically isomorphic to the space Ap,q? (G) and the space of multipliers from Lp? (G) to Lq??-1 (G) is isometrically isomorphic to the dual of the space Ap,q? (G) iff G satisfies a property Pqp. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from L1? (G) to Ap,q? (G) is the space Ap,q? (G).