Function Spaces Related to the Dirichlet Space

Abstract

We present results about spaces of holomorphic functions associated to the classical Dirichlet space. The spaces we consider have roles similar to the roles of $H^1$ and $BMO$ in the Hardy space theory and we emphasize those analogies.

v1: 19 pages

Cited by in corpus (7)

• The Dirichlet space: A Survey
• Factorization in weak products of complete Pick spaces
• The asymptotic shape theorem for generalized first passage percolation
• An $H^p$ scale for complete Pick spaces
• Gaussian analytic functions and operator symbols of Dirichlet type
• Schatten classes of integration operators on Dirichlet spaces
• Bilinear forms on weighted Besov spaces