Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Complex Variables
2024-01-01 v5
Abstract
We characterize the Carleson measures for the Dirichlet space on the bidisc, hence also its multiplier space. Following Maz'ya and Stegenga, the characterization is given in terms of a capacitary condition. We develop the foundations of a bi-parameter potential theory on the bidisc and prove a Strong Capacitary Inequality. In order to do so, we have to overcome the obstacle that the Maximum Principle fails in the bi-parameter theory.
Keywords
Cite
@article{arxiv.1811.04990,
title = {Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc},
author = {Nicola Arcozzi and Pavel Mozolyako and Karl-Mikael Perfekt and Giulia Sarfatti},
journal= {arXiv preprint arXiv:1811.04990},
year = {2024}
}
Comments
57 pages, 5 figures, title changed, minor editing