# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332872

Arkiv for Matematik, 35, (2), 225-251, 1996.5
The\$H\$^{\$p\$}corona problem is the following: Let\$g\$_{1}, ...,\$g\$_{\$m\$}be bounded holomorphic functions with 0<δ≤Σ‖\$g\$_{\$i\$}‖. Can we, for any\$H\$^{\$p\$}function ϕ, find\$H\$^{\$p\$}functions\$u\$_{1}, ...,\$u\$_{\$m\$}such that Σ\$g\$_{\$i\$}\$u\$_{\$i\$}=ϕ? It is known that the answer is affirmative in the polydisc, and the aim of this paper is to prove that it is in non-degenerate analytic polyhedra. To prove this, we construct a solution using a certain integral representation formula. The\$H\$^{\$p\$}estimate for the solution is then obtained by localization and some harmonic analysis results in the polydisc.
```@inproceedings{jörgen1996the\$h\$^{\$p\$}corona,
title={The\$H\$^{\$p\$}corona theorem in analytic polyhedra},
author={Jörgen Boo},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203550580847681},
booktitle={Arkiv for Matematik},
volume={35},
number={2},
pages={225-251},
year={1996},
}
```
Jörgen Boo. The\$H\$^{\$p\$}corona theorem in analytic polyhedra. 1996. Vol. 35. In Arkiv for Matematik. pp.225-251. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203550580847681.