TheH p corona theorem in analytic polyhedra

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 ?, findH ^p functionsu ₁, ...,u _m such that Σg _i u _i =?? 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.