# Intersection d'espaces de Dirichlet à poids harmonique

Translated title of the contribution: Intersection of harmonically weighted Dirichlet spaces

Guanlong Bao, Nihat Gökhan Göğüş, Stamatis Pouliasis

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## Abstract

In 1991, S. Richter introduced harmonically weighted Dirichlet spaces D(μ), motivated by his study of cyclic analytic two-isometries. In this paper, we consider ⋂μ∈PD(μ), the intersection of D(μ) spaces, where P is the family of Borel probability measures. Several function-theoretic characterizations of the Banach space ⋂μ∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.

Translated title of the contribution Intersection of harmonically weighted Dirichlet spaces French 859-865 7 Comptes Rendus Mathematique 355 8 https://doi.org/10.1016/j.crma.2017.07.013 Published - Aug 2017