Abstract. The Radon-Nikodym property for the Banach algebras A r p(G) = Ap ∩ L r (G), where A2(G) is the Fourier algebra, is investigated. A complete solution is given for amenable groups G if 1 <p< ∞ and for arbitrary G if p =2andA2(G) has a multiplier bounded approximate identity. The results are new even for G = R n. 1
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