  This paper can be considered as the sequel of [6], where the authors have
proposed an abstract construction of Hardy spaces H^1. They shew an
interpolation result for these Hardy spaces with the Lebesgue spaces. Here we
describe a more precise result using the real interpolation theory and we
clarify the use of Hardy spaces. Then with the help of the bilinear
interpolation theory, we then give applications to study bilinear operators on
Lebesgue spaces. These ideas permit us to study singular operators with
singularities similar to those of bilinear Calderon-Zygmund operators in a far
more abstract framework as in the euclidean case.
