A note on Dirichlet-type spaces and cyclic vectors in the unit ball of $${\mathbb{C}^2}$$ C 2

Abstract

We extend results of Beneteau, Condori, Liaw, Seco, and the author concerning cyclic vectors in Dirichlet-type spaces to the setting of the unit ball, identifying some classes of cyclic and non-cyclic functions, and noting the necessity of certain capacity conditions.