Geodesic
Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
Discrete analysis (2023)

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arXiv
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.
Publié le : 
Nicola Arcozzi; Pavel Mozolyako; Karl-Mikael Perfekt; Giulia Sarfatti. Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc. Discrete analysis (2023). http://geodesic.mathdoc.fr/item/DAS_2023_a0/
@article{DAS_2023_a0,
     author = {Nicola Arcozzi and Pavel Mozolyako and Karl-Mikael Perfekt and Giulia Sarfatti},
     title = {Bi-parameter {Potential} theory and {Carleson} measures for the {Dirichlet} space on the bidisc},
     journal = {Discrete analysis},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2023_a0/}
}
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AU  - Nicola Arcozzi
AU  - Pavel Mozolyako
AU  - Karl-Mikael Perfekt
AU  - Giulia Sarfatti
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JO  - Discrete analysis
PY  - 2023
UR  - http://geodesic.mathdoc.fr/item/DAS_2023_a0/
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%G en
%F DAS_2023_a0