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 MathÃ©matiques 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 Nehariâ€™s theorem in the unit disc

$\mathbb D$ and Coronaâ€™s Theorem in

$sBMO(\mathbb T^n)$ together with the failure of Nehariâ€™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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