The$H$^{$p$}corona theorem in analytic polyhedra

Jörgen Boo Department of Mathematics, Chalmers University of Technology and Göteborg University

TBD mathscidoc: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.
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@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.
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