Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel
Let \( μ_, b \) be a multilinear commutator generalized by the n-dimensional Marcinkiewicz integral with bounded kernel μ Ώ and let \( b_j Osc__L^r_j \) , 1 ≤ j ≤ m. We prove the following weighted inequalities for ω ∈ A ∞ and 0 < p < ∞: arrayccμ_(f)_L^p(ω )CM(f)_L^p(ω ),& μ_, b (f)array _L^p(ω )CM_L( L)^1/r (f)_L^p(ω ). The weighted weak L(log L)1/r -type estimate is also established for p =1 and ω ∈ A 1., number=4, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Liu, Qingguo and Wu, Jianglong, year=2014, month=Apr., pages=538–550