Mean Lipschitz spaces and a generalized Hilbert operator

If is a positive Borel measure on the interval [0,1) we let H be the Hankel matrix H=(n,k)n,k0 with entries n,k=n+k, where, for n akzk, in the unit disc D. This is a natural generalization of the classical Hilbert operator. In this paper we study the action of the operators H on mean Lipschitz spaces of analytic functions.