BOUNDEDNESS AND COMPACTNESS OF HAUSDORFF OPERATORS ON FOCK SPACES

We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space F-alpha(q) and taking its values into a larger one F-alpha(q), 0 < p <= q <= infinity, as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space F-alpha(infinity) is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become p-summing are also included.