Sharp estimates of the solutions to B{é}zout's polynomial equation and a corona theorem

Abstract

In this paper, we obtain estimates for the solutions to the classical B{é}zout equation that are analogous to Carleson's solution to the corona theorem for the bounded analytic functions on the open unit disk. As an application, we extend some results of Luo and obtain a corona theorem for the multipliers of a class of de Branges--Rovnyak spaces.