# Linus Lidman Bergqvist: Rational inner functions and their Dirichlet type norms

Time: Wed 2021-09-08 13.15 - 14.15

Lecturer: Linus Lidman Bergqvist (Stockholm University)

### Abstract

In this talk, I go through a recent paper in which I study membership of rational inner functions (RIF) in Dirichlet-type spaces in polydisks.

In particular, we prove a theorem relating such inclusions to $$H^p$$ integrability of partial derivatives of a RIF, and as a corollary we prove that all rational inner functions on $$\mathbb{D}^n$$ belong to $$\mathcal{D}_{1/n, \ldots ,1/n}(\mathbb{D}^n)$$.

If time permits, we also show that if $$1/p \in \mathcal{D}_{\alpha,...,\alpha}$$, then the RIF $$\tilde{p}/p \in \mathcal{D}_{\alpha+2/n,...,\alpha+2/n}$$.

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Last changed: Sep 03, 2021