Hardy-Littlewood极大算子的交换子的尖锐加权模不等式

陈艳萍, 韩寒

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 445-452.

PDF(427 KB)
PDF(427 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 445-452. DOI: 10.12386/A2014sxxb0043
论文

Hardy-Littlewood极大算子的交换子的尖锐加权模不等式

    陈艳萍, 韩寒
作者信息 +

Sharp Weighted Norm Inequality for the Commutator of Hardy-Littlewood Maximal Operators

    Yan Ping CHEN, Han HAN
Author information +
文章历史 +

摘要

给出了由Hardy-Little wood极大算子Mb∈BMO生成的m阶交换子的加权模不等式, 并对1<p<2的情况举例证明了其结果是尖锐的.

Abstract

We proved a sharp weighted inequality for the m-the order commutator of the Hardy-Littlewood maximal operator M and b∈BMO Finally we construct an example showing our bound is sharp for the case of 1<p≤2.

关键词

交换子 / Hardy-Littlewood极大算子 / 尖锐加权模不等式

Key words

commutators / Hardy-Littlewood maximal operators / sharp weighted norm inequality

引用本文

导出引用
陈艳萍, 韩寒. Hardy-Littlewood极大算子的交换子的尖锐加权模不等式. 数学学报, 2014, 57(3): 445-452 https://doi.org/10.12386/A2014sxxb0043
Yan Ping CHEN, Han HAN. Sharp Weighted Norm Inequality for the Commutator of Hardy-Littlewood Maximal Operators. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 445-452 https://doi.org/10.12386/A2014sxxb0043

参考文献

[1] Alvarez J., Bagby R., Kurtz D., et al., Weighted estimates for commutators of linear operators, Studia Math., 1993 104: 195-209.
[2] Buckley S. M., Estimates for operator norms on weighted spaces and reverse Jensen inequalities, Trans. Amer. Math. Soc., 1993, 340: 253-272.
[3] Chen X. L., Chen J. C., Weighted BMO estimates for commutators of singular integrals with non-smooth kernels, Acta Mathematica Sinica, Chinese Series, 2012, 55(5): 861-868.
[4] Chung D., Sharp estimates for commutators of the Hilbert, Riesz transforms and the Beurling-Ahlfors operators on weighted Lebesgue spaces, Indiana University Mathematics Journal, 2011, 60(5): 1543-1588.
[5] Chung D., Pereyra C., Pérez C., Sharp bounds for general commutators on weighted Lebesgue spaces, Trans. Amer. Math. Soc., 2012, 364: 1163-1177.
[6] Citti G., Grafakos L., Pérez C., et al., Harmonic and Geometric Analysis, Birkäuser Basel, Birkäuser Editors, 2014.
[7] Coifman R., Fefferman C., Factorization theorems for Hardy spaces in several variables, Annals of Math., 1976, 103: 611-635.
[8] Coifman R., Fefferman C., Weighted norm inequalities for maximal functions and singular integrals, Studia Math., 1974, 51: 241-250.
[9] Cruz-Uribe D., Moen K., Sharp norm inequalities for commutators of classical operators, Publ. Mat., 2012, 56: 147-190.
[10] Ding Y., Weighted boundedness for commutators of fractional integral operators with rough kernel, Journal of Beijing Normal University (Natural Science) (in Chinese), 1996, 32(2): 157-161.
[11] Fefferman C., Stein E. M., Hp spaces of several variables, Acta Math., 1972, 129: 137-193.
[12] Hytönen T., The sharp weighted bound for general Calderón-Zygmund operators, Annal of Math., 2012, 175(3): 1473-1506.
[13] Lerner A., An elementary approach to several results on the Hardy-Littlewood maximal operator, Proc. Amer. Math. Soc., 2008, 136: 2829-2833.
[14] Muckenhoupt B., Norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 1972, 165: 207-226.
[15] Petermichl S., The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical Ap characteristic, Amer. J. Math., 2007, 129: 1355-1375.

基金

国家自然科学基金资助项目(10901017);教育部新世纪人才支持计划(NCET-11-0574);中央高校基本科研业务费专项基金资助
PDF(427 KB)

Accesses

Citation

Detail

段落导航
相关文章

/