Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel
Abstract
Let μΩ,→b be a multilinear commutator generalized by the n-dimensional Marcinkiewicz integral with bounded kernel μ Ώ and let bj ∈OscexpLrj , 1 ≤ j ≤ m. We prove the following weighted inequalities for ω ∈ A ∞ and 0 < p < ∞: ‖μΩ(f)‖Lp(ω)≤C‖M(f)‖Lp(ω),‖μΩ,→b(f)‖Lp(ω)≤C‖ML(logL)1/r(f)‖Lp(ω).The weighted weak L(log L)1/r -type estimate is also established for p =1 and ω ∈ A 1.
Published
25.04.2014
Issue
Section
Research articles
How to Cite
Liu, Qingguo, and Jianglong Wu. “Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals With Bounded Kernel”. Ukrains’kyi Matematychnyi Zhurnal, vol. 66, no. 4, Apr. 2014, pp. 538–550, https://umj.imath.kiev.ua/index.php/umj/article/view/2156.