Sharp weighted estimates for multilinear commutators
Multilinear commutators with vector symbol Formula=(b1,…,bm) defined by Formula are considered, where K is a Calderón–Zygmund kernel. The following a priori estimates are proved for w ∈ A∞. For 0 < p < ∞, there exists a constant C such that Formula and Formula where Formula Formula and ML(log...
| Authors: | , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2002 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47279 |
| Online Access: | http://hdl.handle.net/11441/47279 https://doi.org/10.1112/S0024610702003174 |
| Access Level: | Open access |
| Keyword: | Calderón-Zygmund singular integral operators Commutators Ap weights Maximal functions |
| Summary: | Multilinear commutators with vector symbol Formula=(b1,…,bm) defined by Formula are considered, where K is a Calderón–Zygmund kernel. The following a priori estimates are proved for w ∈ A∞. For 0 < p < ∞, there exists a constant C such that Formula and Formula where Formula Formula and ML(log L)α is an Orlicz type maximal operator. This extends, with a different approach, classical results by Coifman. As a corollary, it is deduced that the operators Formula are bounded on Lp(w) when w ∈ Ap, and that they satisfy corresponding weighted L(log L)1/r-type estimates with w ∈ A1. |
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