Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces

AbstractThe spaces of boundary values of vector-valued functions in Hardy spaces defined by either holomorphic functions on the disk or harmonic functions with maximal function in Lp are characterized in terms of vector-valued measures of bounded p-variation. We extend to the case p = 1 a characterization of the Radon-Nikodym property based on the existence of limits at the boundary for harmonic functions with maximal function in L1. In the case 0 < p ⩽ 1 we find the UMD property as the necessary and sufficient condition to make the spaces defined by maximal function and by conjugate Poisson kernel coincide