A characterization of product BMO by commutators
| dc.creator | Lacey, Michael | |
| dc.creator | Ferguson, Sarah | |
| dc.date | 2001-04-12 | |
| dc.date | 2002-03-22 | |
| dc.date.accessioned | 2026-07-07T04:41:18Z | |
| dc.date.available | 2026-07-07T04:41:18Z | |
| dc.description | Let b be a function on the plane. Let H_j, j=1,2, be the Hilbert transform acting on the j-th coordinate on the plane. We show that the operator norm of the double commutator [[ M_b, H_1], H_2] is equivalent to the Chang-Fefferman BMO norm of b. Here, M_b denotes the operator which is multiplication by b. This result extends a well known theorem of Nehari on weak factorization in the Hardy space H^1 to the same theorem on H^1 of a product domain. The product setting is more delicate because of the presence of a two parameter family of dilations. The method of proof depends upon (a) A dyadic decomposition of product BMO by wavelets (b) a prior estimate of Ferguson and Sadosky involving rectangular BMO (c) and a careful control of certain measures related to those of Carleson. | |
| dc.description | 21 pages. To appear in Acta Math. Appendix corrected | |
| dc.identifier | https://arxiv.org/abs/math/0104144 | |
| dc.identifier | http://arxiv.org/abs/math/0104144 | |
| dc.identifier | Acta Math. {\bf 189} (2002), no.~2, 143--160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61299 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Operator Algebras | |
| dc.title | A characterization of product BMO by commutators | |
| dc.type | text |