MULTIPLIERS AND TENSOR PRODUCTS OF VECTOR VALUED $L^p \left( {G,A} \right)$ SPACES

Abstract

In this paper we define a normed space $A_p^q \left( {G,A} \right)$ and prove some properties of this space. In particular, we show that the space $ L^p \left( {G,A} \right) \otimes _{L^1 \left( {G,A} \right)} L^q \left( {G,A} \right)$ is isometrically isomorphic to the space $A_q^p \left( {G,A} \right)$ and the space of multipliers from $L_{}^p \left( {G,A} \right)$ to $ L_{}^{q'} \left( {G,A^* } \right)$ is isometrically isomorphic to the dual of the space $A_p^q \left( {G,A} \right)$ if $G$ satisfies a property $P_p^q$.