The Dirichlet space on the bi-disc

3 Jul 2021, 14:30


Nikola Arcozzi (University of Bologna)


The Dirichlet space on the bidisc can be informally defined as the tensor product $\mathcal{D} (\mathbb{D}^2) =\mathcal{D} (\mathbb{D}) \otimes \mathcal{D} (\mathbb{D})$ of two copies of the classical holomorphic Dirichlet space. Multipliers and Carleson measures for the space were recently characterized, and the results have been extended to the three-disc, but not to higher powers. Underlying all this there is a new multi-parameter potential theory which is still in its infancy, and many basic problems await an answer. The talk reports on work by several authors: Pavel Mozolyako, Karl-Mikael Perfekt, Giulia Sarfatti, Irina Holmes, Alexander Volberg, Georgios Psaromiligkos, Pavel Zorin-Kranich, and the speaker.

Primary author

Nikola Arcozzi (University of Bologna)

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