The closed range property of dbar on planar domains, part I. Anne-Katrin Gallagher, Oklahoma State University This talk will be accessible to graduate students.
Abstract: Let $\Omega$ be a planar domain in $\mathbb{C}$. We give necessary and sufficient potential-theoretic conditions for the $\overline{\partial}$-operator to have closed range in $L^{2}(\Omega)$. Moreover, we give a new necessary and sufficient potential-theoretic condition for the Bergman space of a $\Omega$ to be infinite dimensional. This work jointly done with Jiri Lebl and Koushik Ramachandran.
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