具有某类Lδ-(logL)ρ核函数的Marcinkiewicz积分交换子的双权估计
Double Weighted Estimates for the Commutator of Marcinkiewicz Integral with Some Lδ-(logL)ρ Kernel
DOI: 10.12677/PM.2020.105068, PDF,    科研立项经费支持
作者: 季颖婷, 陈晓莉*：江西师范大学数学与信息科学学院，江西 南昌
关键词: 交换子；Marcinkiewicz积分；加权Lipschitz函数；Lδ-(logL)ρ条件；Commutator； Marcinkiewicz Integral； Weighted Lipschitz Function； Lδ-(logL)ρ Condition
摘要: 本文证明核函数满足Lδ-(logL)ρ条件的Marcinkiewicz积分μΩ与加权Lipschitz函数b生成的交换子μΩ，b具有(Hp(ω),Lq(ω1-q))和(Hn/n+β(ω),L1,∞)有界性。
Abstract: In this paper, we obtain that the commutator μΩ，b generated by Marcinkiewicz integral μΩ with Lδ-(logL)ρ kernel and weighted Lipschitz function b, has (Hp(ω),Lq(ω1-q)) and (Hn/n+β(ω),L1,∞) boundedness.
文章引用：季颖婷, 陈晓莉. 具有某类Lδ-(logL)ρ核函数的Marcinkiewicz积分交换子的双权估计[J]. 理论数学, 2020, 10(5): 556-565. https://doi.org/10.12677/PM.2020.105068

参考文献

[1] Marcinkiewicze, J. (1938) Sur quelques intégrals de type de Dini. Annales Polonici Mathematici, 17, 42-50.
[2] Stein, E.M. (1958) On the Function of Littlewood-Paley, Lusin and Marcinkiewicze. Transactions of the American Mathematical Society, 88, 430-466.
[3] Lee, J. and Rim, K.S. (2004) Estimates of Marcinkiewicze Integral with Bounded Homogeneous Kernel of Degree Zero. Integral Equations and Operator Theory, 48, 213-223. [Google Scholar] [CrossRef] 
[4] Torchinsky, A. and Wang, S. (1990) A Note on the Marcinkiewicze Integral. Colloquium Mathematicum, 60/61, 235-243.
[5] Ding, Y., Lu, S.Z. and Yabuta, K. (2002) On Commutator of Marcinkiewicze Integral with Rough Kernel. Journal of Mathematical Analysis and Applications, 275, 60-68.
[6] Ding, Y., Lu, S.Z. and Zhang, P. (2004) Weighted Weak Type Estimates for Commutators of Marcinkiewicz Integrals. Science in China, 47, 83-95. [Google Scholar] [CrossRef] 
[7] 王洪彬, 张小瑾, 刘宗光. 一类Marcinkiewicz积分交换子的端点估计[J]. 数学学报A辑, 2008, 51(2): 265-274.
[8] Lin, Y., Liu, Z.G. and Wang, D. (2012) Weighted Endpoint Estimate for Commutator of Marcinkiewicze Integral. Pan-American Mathematical Journal, 22, 105-116.
[9] 陆善镇, 吴强, 杨大春. 交换子在Hardy空间上的有界性[J]. 中国科学A辑, 2002, 32(2): 232-244.
[10] Wang, H. (2016) Estimates of Some Integral Operators with Bounded Variable Kernels on the Hardy and Weak Hardy Spaces over Rn. Acta Mathematica Sinica, English Series, 32, 411-438. [Google Scholar] [CrossRef] 
[11] Carcia-Cuerva, J. and Rudio De Francia, J.L. (1958) Weighted Norm Inequalities and Related Topics. North-Holland Math, Amsterdam. [Google Scholar] [CrossRef] 
[12] Garca-Cuerva, J. (1979) Weighted Hp Space. Dissertation Summaries in Mathematics, 162, 1-63.
[13] 黄菲. Marcinkiewicz~积分交换子和多线性平方算子交换子的有界性[D]: [硕士学位论文]. 南昌: 江西师范大学, 2017.
[14] 李爽. Marcinkiewicz积分及其交换子的加权范数不等式[D]: [硕士学位论文]. 南昌: 江西师范大学, 2018.

为你推荐