Cyclicity and iterated logarithms in the Dirichlet space

Alexandru Aleman, Stefan Richter

Let $D(\hat{I}¼)$ denote a harmonically weighted Dirichlet space on the unit disc $\mathbb{D}$. We show that outer functions $f\in D(\hat{I}¼)$ are cyclic in $D(\hat{I}¼)$, whenever $\log f$ belongs…