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Journal of the London Mathematical Society 2002 65(3):672-692; doi:10.1112/S0024610702003174
© 2002 by London Mathematical Society
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© The London Mathematical Society

Sharp Weighted Estimates for Multilinear Commutators

C. Pérez and R. Trujillo-González

Departmento de Análisis Matematico, Facultad de Matemáticas, Universidad de Sevilla 41080 Sevilla, Spain, carlos.perez{at}uam.es
Departmento de Análisis Matemático, Universidad de La Laguna 38271 La Laguna, S/C de Tenerife, Spain, rotrujil{at}ull.es

Received 15 June 2000. Revision received 26 June 2001.

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 isin A{infty}. For 0 < p < {infty}, there exists a constant C such that


Formula

and


Formula

where


Formula


Formula

and ML(log L){alpha} 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 isin Ap, and that they satisfy corresponding weighted L(log L)1/r-type estimates with w isin A1.


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