Acta mathematica scientia,Series B ›› 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

 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)

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

CLC Number: 

  • 60G42
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