Big Hankel operators on Hardy spaces of strongly pseudoconvex domains

In this article, we investigate the (big) Hankel operator H f on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂ n . 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 H 2 (Ω) of other pseudoconvex domains. In these arguments, Amar’s L p -estimations and Berndtsson’s L 2 -estimations for solutions of the ∂̅_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.