A Korenblum Maximum Principle for weighted Hilbert spaces of entire Dirichlet series with real frequencies

Abstract

In this paper, we study a Korenblum Maximum Principle for weighted Hilbert spaces of entire Dirichlet series with real frequencies. We investigate dominating sets for which the Korenblum Maximum Principle must hold. The results obtained imply that a dominating set, if exists, must be a left half-plane. This provides a new perspective for studying Korenblum Maximum Principle on function spaces containing the entire Dirichlet series.