Hilbert type operators acting from the Bloch space into Bergman spaces

Let mu be a finite positive Borel measure on [0,1) and alpha>-1. The generalized integral operator of Hilbert type I(mu alpha+1)is defined on the spaces H(D) of analytic functions in the unit disc D as follows: I mu alpha+1(f)(z) =integral(1)(0)f(t) / (1-tz)alpha+1d mu(t), f is an element of H(D), z is an element of D. <br /> In this paper, we give a unified characterization of the measures mu for which the operator I mu alpha+1 is bounded from the Bloch space to a Bergman space for all alpha>-1. Additionally, we also investigate the action of I(mu alpha+1 )from the Bloch space to the Hardy spaces and the Besov spaces.