Mixed de Branges–Rovnyak and sub-Bergman spaces

Abstract

In this paper we obtain some general results about mixed second order de Branges–Rovnyak spaces defined by an operator A such that both A and A⁎ are 2-hypercontractions. As applications of these results, we study mixed second order sub-Bergman spaces since the analytic Toeplitz operator Tb on weighted Bergman space Aα2 for α≥0 on the unit disk is such that both Tb and Tb⁎ are 2-hypercontractions.