Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Authors

  • Qingguo Liu
  • Jianglong Wu

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 ≤ jm. We prove the following weighted inequalities for ωA and 0 < p < ∞: μΩ(f)Lp(ω)CM(f)Lp(ω),μΩ,b(f)Lp(ω)CML(logL)1/r(f)Lp(ω).

The weighted weak L(log L)1/r -type estimate is also established for p =1 and ωA 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.