Abstract
We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. More specifically, given and , where , we prove that there exists a distributionally irregular entire function f for the operator D such that its p-integral mean function grows not more rapidly than . This completes related known results about the possible rates of growth of such means for D-hypercyclic entire functions. It is also obtained, the existence of dense linear submanifolds of all whose ***nonzero vectors are D-distributionally irregular and present the same kind of growth. Furthermore, the D-distributional irregularity in weighted Banach spaces of entire functions is analysed.
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