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arXiv · 1811.04990

Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc

Nicola Arcozzi·Pavel Mozolyako·Karl-Mikael Perfekt·Giulia Sarfatti
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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.

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Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, Giulia Sarfatti. 2018-11-12. Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc. https://arxiv.org/abs/1811.04990

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