Cyclicity in the Dirichlet space

Abstract

Let \(\mathcal{D}\) be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We give a new sufficient condition, not far from the known necessary condition, for a function f∈\(\mathcal{D}\) to be cyclic, i.e. for {pf: p is a polynomial} to be dense in \(\mathcal{D}\).