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| 非齐型空间中一类满足Hörmander条件的Marcinkiewicz交换子估计 | |
| 引用本文： | 李亮,江寅生.非齐型空间中一类满足Hörmander条件的Marcinkiewicz交换子估计[J].数学学报,2010,53(1):87-96. |
| 作者姓名： | 李亮 江寅生 |
| 作者单位： | 1. 伊犁师范学院数学系应用数学研究所 伊宁 835000; 2. 新疆大学数学与系统科学学院 乌鲁木齐 830046 |
| 基金项目： | 国家自然科学基金(10861010);新疆高校科研计划(XJEDU2008S58);伊犁师范学院科研项目 |
| 摘 要： | 记μ为 上的非负Radon测度,且仅满足对固定的C0>0和n∈(0,d],及所有的 和r>0, μ(B(x,r))≤C0 rn.作者建立了一类核函数满足Hörmander条件的Marcinkiewicz积分与Lipβ(μ)(0<β)函数生成的交换子由Lp(μ)到Lq(μ),由Lp(μ) 到Lipβ-n/p(μ)及Ln/β(μ)到RBMO(μ)有界.部分结论对经典 Marcinkiewicz积分也是新的.
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| 关 键 词： | 非倍测度 Marcinkiewicz积分 Lipβ(μ)函数 |
| 收稿时间： | 2008-11-26 |
| 修稿时间： | 2009-04-09 |
Estimates for Commtators of Marcinkiewicz Integrals with Hörmander-Type Condition in Non-Homogeneous Spaces |
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| Institution: | 1. Department of Mathematics, Institute of Applied Mathematics, ILi Normal University, Yining 835000, P. R. China; 2. College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China |
| Abstract: | Let μ be a positive Radon measure on which may be non doubling. The only condition that μ must satisfy is μ(B(x,r))≤C0 rn for all , r>0 and some fixed n∈(0,d]. In this paper, the authors establish the boundedness of the commutator generated by the Lipβ(μ)(0<β) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger Hörmander-type condition, respectively, from Lp(μ) to Lq(μ) with 1<p≤n/β and 1/q=1/p-β/n, from the space Lp(μ) to Lipβ-n/p(μ) and from the space Ln/β(μ) to RBMO(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
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| Keywords: | doubling measure Marcinkiewicz integral Lip&beta (&mu ) |
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