  In this paper we study Hardy spaces associated with non-negative self-adjoint
operators and develop their vector-valued theory. The complex interpolation
scales of vector-valued tent spaces and Hardy spaces are extended to the
endpoint p=1. The holomorphic functional calculus of L is also shown to be
bounded on the associated Hardy space H^1_L(X). These results, along with the
atomic decomposition for the aforementioned space, rely on boundedness of
certain integral operators on the tent space T^1(X).
