$\mathcal{H}^p$-corona problem and convex domains of finite type

TL;DR

This paper proves that the $ ext{H}^p$-corona problem can be solved for convex domains of finite type in complex n-dimensional space, extending the understanding of holomorphic function theory in these domains.

Contribution

It establishes the solvability of the $ ext{H}^p$-corona problem specifically for convex finite type domains in higher-dimensional complex spaces.

Findings

Solution exists for the $ ext{H}^p$-corona problem in convex finite type domains.

Extends previous results to higher dimensions and broader classes of domains.

Provides new techniques for solving corona problems in complex analysis.

Abstract

We prove that the $\mathcal{H}^p$-corona problem has a solution for convex domains of finite type in $\mathbb{C}^n$, $n \ge 2$.