Weighted contractivity for derivatives of functions in the Bergman space on the unit disk

Abstract

In a recent paper, Ramos and Tilli proved certain sharp inequality for analytic functions in subdomains of the unit disk. We will generalize their main inequality for derivatives of functions from Bergman space with respect to two diferent measures. Some connections with an analog for the Fock spaces, earlier investigated in Kalaj, will also be discussed.

18 pages. arXiv admin note: text overlap with arXiv:2205.07998 by other authors; it has been accepted for publication in Computational Methods and Function Theory