数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 279-289.doi: 10.1016/S0252-9602(12)60210-0

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TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES

张传洲*|张学英   

  1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process
    (Wuhan University of Science and Technology), Wuhan 430081, China
  • 收稿日期:2011-03-21 修回日期:2011-11-25 出版日期:2013-01-20 发布日期:2013-01-20
  • 通讯作者: 张传洲,zczwust@163.com E-mail:zczwust@163.com;zhxying315@sohu.com
  • 基金资助:

    This work was supported by National Natural Science Foundation of China (11201354), Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201121), National Natural Science Foundation of Pre-Research Project (2011XG005) and also supported by Natural Science Fund of Hubei Province (2010CDB03305), Wuhan Chenguang Program (201150431096), Open Fund of State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing (11R01).

TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES

 ZHANG Chuan-Zhou*, ZHANG Xue-Ying   

  1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process
    (Wuhan University of Science and Technology), Wuhan 430081, China
  • Received:2011-03-21 Revised:2011-11-25 Online:2013-01-20 Published:2013-01-20
  • Contact: ZHANG Chuan-Zhou,zczwust@163.com E-mail:zczwust@163.com;zhxying315@sohu.com
  • Supported by:

    This work was supported by National Natural Science Foundation of China (11201354), Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201121), National Natural Science Foundation of Pre-Research Project (2011XG005) and also supported by Natural Science Fund of Hubei Province (2010CDB03305), Wuhan Chenguang Program (201150431096), Open Fund of State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing (11R01).

摘要:

In [1] the boundedness of one dimensional maximal operator of dyadic deriva-tive is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space Hq to the Hardy space Hq for 0 < q ≤ 1 and is bounded from pα , Dα to Lα for some α.

关键词: Hardy space, dyadic derivative, dyadic integral

Abstract:

In [1] the boundedness of one dimensional maximal operator of dyadic deriva-tive is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space Hq to the Hardy space Hq for 0 < q ≤ 1 and is bounded from pα , Dα to Lα for some α.

Key words: Hardy space, dyadic derivative, dyadic integral

中图分类号: 

  • 42C10