H^p-estimates of holomorphic division formulas

Mats Andersson and Hasse Carlsson

Vol. 173 (1996), No. 2, 307–335

DOI: 10.2140/pjm.1996.173.307

Abstract

We prove that an explicit formula, due to Berndtsson, for representation of solutions of holomorphic division problems in a strictly pseudoconvex domain admit H^p-estimates and provides a solution to the following problem: Given bounded holomorphic functions G₁,…,G_m such that ∑ |G_j|² ≥ δ², and ϕ ∈ H^p, find u_j ∈ H^p such that ∑ G_ju_j = ϕ. The estimates are based on careful estimates of Hefer functions and a T1-theorem for Carleson measures, due to Christ and Journé.

Mathematical Subject Classification 2000

Primary: 32A37

Secondary: 32A35, 32F20

Milestones

Received: 18 August 1993

Revised: 15 June 1994

Published: 1 April 1996