Operators into Hardy spaces and analytic Pettis integrable functions **This research has been supported by DGICYT grant PB96-1327

We present some recent results on operators with values in Hardy spaces and vector valued functions. Some compact operators are constructed which are not representable by functions and the non coincidence of the vector valued Hardy spaces with either the projective or the injective tensor product is proved. We improve some previous results on the failure of Fatou’s theorem on radial almost everywhere convergence for analytic Pettis integrable functions.