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Weighted estimates for multilinear commutators of Marcinkiewicz integral

Authors:

Pu Zhang

Affiliation:

(1) Department of Mathematics, Mudanjiang Teachers College, Mudanjiang, 157012, P. R. China

Abstract:

Let μ be the n-dimensional Marcinkiewicz integral and μ_b→ the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A _∞ and 0 < p < ∞,

$||\mu (f)||_{L^p (\omega )} \leqslant C||Mf||_{L^p (\omega )} and||\mu _{\vec b} (f)||_{L^p (\omega )} \leqslant C||M_{L(logL)^{{1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r}} } f||_{L^p (\omega )} .$

The weighted weak L(log L)^1/r-type estimate is also established when p = 1 and ω ∈ A ₁. Supported by Hei Long Jiang Postdoctoral Foundation (LBH-Q06002)

Keywords:

Marcinkiewicz integral multilinear commutator sharp function A p weights

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