Abstract
TheH p corona problem is the following: Letg 1, ...,g m be bounded holomorphic functions with 0<δ≤Σ‖g i ‖. Can we, for anyH p function ϕ, findH p functionsu 1, ...,u m such that Σg 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. TheH p estimate for the solution is then obtained by localization and some harmonic analysis results in the polydisc.
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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.
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Boo, J. TheH p corona theorem in analytic polyhedra. Ark. Mat. 35, 225–251 (1997). https://doi.org/10.1007/BF02559968
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DOI: https://doi.org/10.1007/BF02559968