A Hankel matrix acting on spaces of analytic functions.

Abstract

If μ is a positive Borel measure on the interval [0, 1) we let H_μ be the Hankel matrix { μ_{n,k} }_{n,k} with entries μ_{n,k} =μ_{n+k}, where, for 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 improve the results obtained in some recent papers concerning the action of the operators H_μ on Hardy spaces and on Möbius invariant spaces.