Multipliers and tensor products of weighted L-p-spaces

Abstract

Let G be a locally compact unimodular group with Haar measure rmdx and Le be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space A(omega)(p,q) (G) and prove that A(omega)(p,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 A(omega)(p,q) (G) admits an approximate identity bounded in L-1 omega (G). It is also proved that the space L-omega(p) (G) x (L1 omega) L-omega(q) (G) is isometrically isomorphic to the space A(omega)(p,q) (G) and the space of multipliers from L-omega(p) (G) to L-omega -1(q') (G) is isometrically isoinorphic to the dual of the space A(omega)(p,q) (G) iff G satisfies a property P-p(q). 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 L-omega(1) (G) to A(omega)(p,q) (G) is the space A(omega)(p,q) (G).