On commutators of Marcinkiewicz integrals with rough kernel
On commutators of Marcinkiewicz integrals with rough kernel
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DOI：
10.1016/s0022-247x(02)00230-5
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发表时间：
2002-11
影响因子：
1.3
通讯作者：
Yong Ding;Shan-zhen Lu;K. Yabuta
中科院分区：
文献类型：
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作者：
Yong Ding;Shan-zhen Lu;K. Yabuta
在本文中，我们证明高阶换向器 μmΩ,b, μ*,mΩ,λ,band μmΩ,S,在加权 Lp 空间上包含所有有界算子。这些换向器分别由 BMO ( Rn) 函数 b(x) 和一类粗 Marcinkiewicz 积分算子 μΩ、μ*Ω,λ 和 μΩ,S 构成，分别对应于 Littlewood-Paley g 函数、Littlewood-Paley g*λ 函数和 Lusin 面积积分。本文的结果是 Torchinsky 和 Wang (1990) 以及 Alvarez 等人的结果的本质改进和扩展。 （1993）。
In this note we prove that the higher-order commutators μmΩ,b, μ∗,mΩ,λ,band μmΩ,S,bare all of bounded operators on the weighted Lpspaces. These commutators are formed respectively by a BMO ( Rn) function b(x) and a class of rough Marcinkiewicz integral operators μΩ, μ∗Ω,λand μΩ,S, which are corresponding to the Littlewood–Paley g-function, Littlewood–Paley g∗λ-function and the Lusin area integral, respectively. The results in this paper are essential improvements and extensions of the results by Torchinsky and Wang (1990) and by Alvarez et al. (1993).