On Hankel operators on Hardy and Bergman spaces and related questions

. In this partly expository paper we analyze the (small) Hankel operator h b on Hardy and Bergman spaces on a class of smoothly bounded domains of finite type in C n which includes the strictly pseudoconvex domains and the convex domains. Wecompletely characterize the Hankel operators h b that are bounded, compact, and belong to the Schatten ideal S p , for 0 < p < ∞ , 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 H 1 ( Ω ) and A 1 ( Ω ) respectively, results that are of independent interest.

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