On Hankel operators on Hardy and Bergman spaces and related questions

In this partly expository paper we analyze the (small) Hankel operator hb on Hardy and Bergman spaces on a class of smoothly bounded domains of finite type in Cn which includes the strictly pseudoconvex domains and the convex domains. We completely characterize the Hankel operators hb that are bounded, compact, and belong to the Schatten ideal Sp, for 0 < ∞, for this class of domains, generalizing the results of [BPS2]1 where such results have been obtained when Ω is a convex domain of finite type. We describe the main ideas of the proofs which are basically the same as in [BPS2], and present some extensions and generalizations. In order to characterize the bounded Hankel operators, we prove factorization theorems for functions in H1(Ω) and A1(Ω) respectively, results that are of independent interest.