Mean Lipschitz spaces and a generalized Hilbert operator.

Abstract

If μ is a positive Borel measure on the interval [0, 1) we let H_μ be the Hankel matrix H_μ={ μ_{n,k} }_{n,k} with entries μ_{n,k} =μ_{n+k} where μ_n denotes the moment of order n of μ. This matrix induces formally an operator on the space of all analytic functions 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_μ on mean Lipschitz spaces of analytic functions.