Optimal growth of upper frequently hypercyclic functions for some weighted Taylor shifts

Abstract

We are interested in the optimal growth in terms of $L^p$-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic function on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between the $\mathcal{U}$-frequent hypercyclicity and the hypercyclicity.

Correction of a small common mistake in the proofs of Propositions 4.9, 5.5 and 5.9 (adding a division by the coefficient α_k)