数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 268-280.doi: 10.1016/S0252-9602(11)60227-0

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BOUNDEDNESS OF DYADIC DERIVATIVE AND CESÀRO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES

陈丽红, 刘培德   

  1. College of Science, Wuhan Textile |University, |Wuhan 430073, |China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2008-10-16 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    This work was supported by the Nation Natural Science Foundation of China (10671147) and Wuhan University of Science and
    Engineering under grant (093877)

BOUNDEDNESS OF DYADIC DERIVATIVE AND CESÀRO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES

 CHEN Li-Hong, LIU Pei-De   

  1. College of Science, Wuhan Textile |University, |Wuhan 430073, |China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2008-10-16 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    This work was supported by the Nation Natural Science Foundation of China (10671147) and Wuhan University of Science and
    Engineering under grant (093877)

摘要:

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Ces`aro mean operator σ* are bounded from the B-valued martingale Hardy spaces pα, Dα, pLα, p ˜H?α , pKr to Lα (0 < α < 1), respectively. The facts show that it depends on the geometrical properties of the Banach space.

关键词: B-valued martingale, martingale space, dyadic derivative, dyadic integral

Abstract:

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Ces`aro mean operator σ* are bounded from the B-valued martingale Hardy spaces pα, Dα, pLα, p ˜H?α , pKr to Lα (0 < α < 1), respectively. The facts show that it depends on the geometrical properties of the Banach space.

Key words: B-valued martingale, martingale space, dyadic derivative, dyadic integral

中图分类号: 

  • 60G42