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

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