Lectures on Nehari's Theorem on the Polydisk

Details Lectures on Nehari's Theorem on the Polydisk Lectures on Nehari's Theorem on the Polydisk

2006-01-12

arxiv.org/abs/math/0601272v1

Mathematics

Classical Analysis and ODEs

35 pages. 65 References

Scientific paper

We give a leisurely proof of a result of Ferguson--Lacey (math.CA/0104144) and Lacey--Terwelleger (math.CA/0601192) on a Nehari theorem for "little" Hankel operators on a polydisk. If H_b is a little Hankel operator with symbol b on product Hardy space we have || H_b || \simeq || b ||_{BMO} where BMO is the product BMO space identified by Chang and Fefferman. This article begins with the classical Nehari theorem, and presents the necessary background for the proof of the extension above. The proof of the extension is an induction on parameters, with a bootstrapping argument. Some of the more technical details of the earlier proofs are now seen as consequences of a paraproduct theory.

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