Growth of frequently or log-frequently hypercyclic functions

We obtain the optimal boundary behavior of the log-frequently hypercyclic functions with respect to the Taylor shift acting on H(D) in terms of average L-p-norms. In passing we establish some new results on the growth of frequently or log-frequently hypercyclic functions for the differentiation operator on H(C). All these results highlight the similarities and the differences between the lower and upper bounds on the growth of frequently and log-frequently hypercyclic functions, on the one hand in the case of the Taylor shift operator on H(D) and on the other hand in the case of the differentiation operator on H(C). (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study explores the optimal boundary behavior of log-frequently hypercyclic functions with respect to the Taylor shift on H(D) using average L-p-norms, and also examines the growth of frequently or log-frequently hypercyclic functions for the differentiation operator on H(C). These results highlight the similarities and differences between the lower and upper bounds on the growth of frequently and log-frequently hypercyclic functions under different operators on different function spaces.