Wolff type estimates and the Hp corona problem in strictly pseudoconvex domains

Abstract

LetD be a strictly pseudoconvex domain in Cⁿ. We prove that $\bar \partial u = \phi , \phi $ , ϕ a $\bar \partial $ (0,1)-form, admits solutions in L^p(∂D), 1≤p<∞ and in BMO, under certain Wolff type conditions of ϕ. Some such results (for 1< p<∞) have previously been obtained by Amar in the ball, but under slightly stronger hypotheses. As a corollary we obtain a H^p-corona result for two generators.