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). [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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
