Abstract
TheHp corona problem is the following: Let g1, ..., gm be bounded holomorphic functions with 0<δ≤Σ‖gi‖. Can we, for any Hp function ϕ, find Hp functions u1, ..., um such that Σgiui=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 Hp estimate for the solution is then obtained by localization and some harmonic analysis results in the polydisc.
Note
I am very grateful to my advisor, Mats Andersson, for proposing the subject of this paper and for showing great interest in the project. I also want to express my thanks to Hasse Carlsson and Joaquim Ortega Cerdà for many helpful discussions. Finally, I wish to thank the referee for several comments which helped to improve the exposition.
Citation
Jörgen Boo. "The Hp corona theorem in analytic polyhedra." Ark. Mat. 35 (2) 225 - 251, October 1997. https://doi.org/10.1007/BF02559968
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