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Homological properties of several Banach left L1(G)-modules have been studied by Dales and Polyakov and recently by Ramsden. In this paper, we characterize some homological properties of 
and 
as Banach left L1(G)-modules, such as flatness, injectivity and projectivity.
Let A be a commutative Banach algebra with identity of norm 1, X a Banach A-module and G a locally compact abeian group with Haar measure. Then the multipliers from an A -valued function algebra into an X-valued function space is studied. We characterize the multiplier spaces as the following isometrically isomorphic relations under some appropriate conditions:
