Big Hankel operators on Hardy spaces of strongly pseudoconvex domains

Abstract

In this article, we investigate the (big) Hankel operator H_f on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂⁿ. We observe that H_f is bounded on H^p (Ω) (1 < p < ∞) if f belongs to BMO and we obtain some characterizations for H_f on H² (Ω) of other pseudoconvex domains. In these arguments, Amar’s L^p-estimations and Berndtsson’s L²-estimations for solutions of the \({{\bar \partial }_b}\) -equation play a crucial role. In addition, we solve Gleason’s problem for Hardy spaces H^p(Ω) (1 ≤ p ≤ ∞) of bounded strongly pseudoconvex domains.