Recovering Product BMO from Schatten Hankel operators

Abstract

We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p<\infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's theorem holds under the hypothesis that the operator belongs to a Schatten class.

Ver2: Added a remark after Theorem 1.1. Fixed a typo in the statement of Lemma 3.1