数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1092-1101.

• 论文 • 上一篇    下一篇

变指标Lebesgue空间上的Marcinkiewicz积分高阶交换子

王洪彬1,3, 傅尊伟2, 刘宗光3   

  1. 1.淄博师范高等专科学校数理科学系 山东淄博 255130|2.临沂大学数学系 山东 临沂 276005|3.中国矿业大学(北京) 数学系 北京 100083
  • 收稿日期:2010-12-21 修回日期:2012-03-15 出版日期:2012-12-25 发布日期:2012-12-25
  • 基金资助:

    国家自然科学基金(10901076, 10871024, 11171345)、中央高校基本科研业务费专项资金(2010YS01) 和山东省自然科学基金(Q2008A01)资助

Higher-order Commutators of Marcinkiewicz Integrals on Variable Lebesgue Spaces

 WANG Hong-Bin1,3, FU Zun-Wei2, LIU Zong-Guang3   

  1. 1.Department of Mathematical and Physical Science, Zibo Normal College, Shandong Zibo 255130;
    2.Department of Mathematics, Linyi University, Shandong Linyi 276005;
    3.Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083
  • Received:2010-12-21 Revised:2012-03-15 Online:2012-12-25 Published:2012-12-25
  • Supported by:

    国家自然科学基金(10901076, 10871024, 11171345)、中央高校基本科研业务费专项资金(2010YS01) 和山东省自然科学基金(Q2008A01)资助

摘要:

证明了一类Marcinkiewicz积分高阶交换子在变指标Lebesgue空间上的BMO和Lipschitz估计, 对于分数次积分交换子也得到了类似的结果.

关键词: 交换子, Marcinkiewiz积分, 分数次积分, 变指标Lebesgue空间

Abstract:

In view of weak estimates, we show the BMO and Lipschitz estimates for higher-order commutators of a class of Marcinkiewicz integrals, which correspond  to the Littlewood-Paley g function, Littlewood-Paley g*λ function and the Lusin area integral on the variable Lebesgue space. The similar results for commutators of fractional integrals are also discussed.

Key words: Commutator, Marcinkiewiz integral, Fractional integral, Variable Lebesgue space

中图分类号: 

  • 42B20