Nicola Arcozzi. Potential theory in product spaces: some results and some questions

Recently some new tools in bi-parameter potential theory have been developed in order to characterize the multiplier space for the holomorphic Dirichlet space on the bi-disc: a strong capacitary inequality and a Mazya-type trace inequality. It is natural to ask how much of classical potential theory can be carried out in this new context. Problems of a basic nature abound, and known techniques seem to be of little help. (I mostly talk of work in collaboration with Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti).