The Fourier Algebra of a Measured Groupoid and Its Multipliers

The classical definitions of the Fourier algebrasB(G) andA(G) of a locally compact group are extended to an arbitrary measured groupoidG. Dualities are established betweenB(G) andA(G) and the convolution algebrasC*μ(G) andVN(G) in the framework of operator modules. They are used to generalize results of Varopoulos and Pisier about Littlewood functions and completely bounded multipliers.