On the maximal ideal space of $H^\infty(B)$

TL;DR

This paper addresses the corona problem in complex analysis, providing affirmative solutions for the unit ball and polydisc in multiple complex variables, advancing understanding of maximal ideal spaces in these contexts.

Contribution

It offers new affirmative solutions to the corona problem for the unit ball and polydisc, expanding the class of domains where the problem is solved.

Findings

Confirmed the corona problem has an affirmative solution on the unit ball.

Confirmed the corona problem has an affirmative solution on the unit polydisc.

Abstract

We study the corona problem on the unit ball and the unit polydisc in $\CC^n$. We provide affirmative solutions to both problems.