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.
Bi-parameter Potential Theory and Carleson Measures for the Dirichlet Space on the Bidisc / Arcozzi, Nicola; Mozolyako, Pavel; Perfekt, Karl-Mikael; Sarfatti, Giulia. - In: DISCRETE ANALYSIS. - ISSN 2397-3129. - 2023:(2023). [10.19086/da.91187]
Bi-parameter Potential Theory and Carleson Measures for the Dirichlet Space on the Bidisc
Giulia Sarfatti
2023-01-01
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.| File | Dimensione | Formato | |
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