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Seminar on Analysis, Differential Equations and Mathematical Physics
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Bi-parameter Potential theory and some applications to holomorphic spaces N. Arcozzi Department of Mathematics, University of Bologna |
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Abstract: The bidisc carries its own natural Potential Theories, which are not developed in depth. The main obstructions are the lack of the usual basic tools: covering theorems, maximum principles, inequalities for weighted maximal functions... In the case of the bi-disc, we prove a Capacitary Strong Inequality and deduce from it a characterization of the trace inequalities for a Bessel Potential Space. As a consequence, we characterize the multipliers for the Holomorphic Dirichlet Space on the bidisc. Work in collaboration with Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti. Language: English Website: https://msrn.tilda.ws/sl |