Intersection of harmonically weighted Dirichlet spaces

In 1991, S. Richter introduced harmonically weighted Dirichlet spaces D(mu), motivated by his study of cyclic analytic two-isometries. In this paper, we consider boolean AND(mu is an element of P) D(mu), the intersection of D(mu) spaces, where Pis the family of Borel probability measures. Several function-theoretic characterizations of the Banach space boolean AND(mu is an element of P) D(mu) are given. We also show that boolean AND(mu is an element of P) D(mu) is located strictly between some classical analytic Lipschitz spaces and boolean AND(mu is an element of P) D(mu) can be regarded as the endpoint case of analytic Morrey spaces in some sense. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.