A Hankel Matrix Acting on Spaces of Analytic Functions

If mu is a positive Borel measure on the interval [0, 1) we let H-mu be the Hankel matrix H-mu = (mu(n, k))(n, k >= 0) with entries mu(n, k) = mu(n+k), where, for n = 0, 1, 2, ... , mu(n) denotes the moment of order n of mu. This matrix induces formally the operator H-mu(f)(z) = Sigma(infinity)(n = 0) (Sigma(infinity)(k = 0) mu(n), (k)a(k)) z(n) on the space of all analytic functions f(z) = Sigma(infinity)(k=0) a(k)z(k), in the unit disc D. This is a natural generalization of the classical Hilbert operator. In this paper we improve the results obtained in some recent papers concerning the action of the operators H-mu on Hardy spaces and on Mobius invariant spaces.