On the corona problem for strongly pseudoconvex domains
The author studies the corona problem on domains where the \(\overline{\partial}\)-equation can be solved with uniform bounds. This class includes for example strictly pseudoconvex domains. The main result is that on such a domain, if the sublevel sets of the corona data have have closures (in \(\mathbb{C}^n\) !) whose intersection is empty, then the corona problem has a solution. This extends a result of \textit{S. G. Krantz} [Proc. Am. Math. Soc. 138, No. 10, 3651--3655 (2010; Zbl 1204.32004)] that treated this setup with two pieces of data. Both papers use the Koszul complex associated to the corona data, combined with \(\overline{\partial}\)-techniques.
scientific article; zbMATH DE number 7644655
scientific article