Three Classification Results In The Theory Of Weighted Hardy Spaces On The Ball

Abstract

We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which of them satisfy that subsets of the ball yield isometrically isomorphic subspaces if and only if there is an analytic automorphism of the ball taking one to the other. We also characterize pairs of weighted Hardy spaces on the unit disk which are isomorphic via a composition operator by a simple criterion on their respective sequences of weights.