MULTIPLIERS OF BANACH-VALUED FUNCTION SPACES ON LCA GROUP

Let G be a locally compact abelian (LCA) group with Haar measure dt and dual group (G) over cap. Let A be a commutative Banach algebra, X and Y Banach spaces with A-module. Denote by L-1 (G, A) the space of all Bochner integrable A-valued functions defined on G. It is a commutative Banach algebra under convolution. L-P (G, X) denotes the space of all X-valued measurable functions defined on G whose X-norms are in usual L-P space, it is a Banach space for each p, 1 <= p < infinity. In this paper, we characterize the multiplier operators of various Banach-valued functions defined on G to be function spaces. The homomorphism A-module multipliers of X into Y is established in the forms of A replaced by L-1(G, A); X by L-1(G, X); Y by L-P(G, Y) and Y* by L-q(G,Y*), 1/p + 1/q and 1 < p, q < infinity where the applications of the Radon-Nikodym property (RNP) in wide sense are concerned.