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Journal of Operator Theory

Volume 33, Issue 2, Spring 1995  pp. 223-233.

Big Hankel operator and $\bar \partial _b$-equation

Authors Eric Amar
Author institution: Laboratoire de Mathématiques Pures, Universite de Bordeaux I, 351, Cours de la Liberation, 33405 Talence, FRANCE

Summary:  We establish links between Hankel operators theory and $\bar \partial _b$ equation in one and several variables. This leads to proofs of the classical Nehari’s theorem in the unit disc $\mathbb D$ and Corona’s Theorem in $sBMO(\mathbb T^n)$ together with the failure of Nehari’s theorem for the Bergman class on $\mathbb D$ and for the Hardy class on the unit polydisc or the unit ball in $\mathbb C^n$, $n \ge 2$.

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