\(H^ p\)-estimates of holomorphic division formulas
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 \(G_1, \dots, G_m\) such that \(\sum |G_j |^2 \geq\delta^2\), and \(\varphi \in H^p\), find \(u_j \in H^p\) such that \(\sum G_ju_j = \varphi\). The estimates are based on careful estimates of Hefer functions and a \(T1\)-theorem for Carleson measures, due to Christ and Journé.
scientific article; zbMATH DE number 940728