Growth of hypercyclic functions: a continuous path between -frequent hypercyclicity and hypercyclicity

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