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Weighted estimates for maximal multilinear commutators

✍ Scribed by Pu Zhang

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
240 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let T be a Calderón–Zygmund operator with regular kernel K and T *~b~ be the maximal multilinear commutator defined by
equation image
.

In this paper, the following weighted estimates for T *~b~ are discussed. Precisely, for 0 < p < ∞, ω ∈ A ~∞~ and b ~j~ ∈ Osc , r~j~ ≥ 1, j = 1, … , m , there exists a positive constant C such that
equation image
.

For p = 1 and ω ∈ A ~1~, the weighted weak L (log L )^1/r^ ‐type estimates are also established.

Our theorems are parallel to the ones of the multilinear commutators of Calderón–Zygmund operators obtained in [18] and extend the main result in [14] essentially. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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