Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (2): 265-275.doi: 10.1016/S0252-9602(09)60027-8

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THE DYADIC DERIVATIVE AND CESÀRO MEAN OF BANACH-VALUED MARTINGALES

CHEN Li-Gong, LIU Pei-De   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China College of Science, Wuhan University of Science and Engineering Wuhan 430073, China
  • Received:2006-09-17 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    This work was supported by the National Natural Science Foundation of China (10371093)

Abstract:

In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic  erivative of the dyadic integral and Ces`aro means are bounded from the dyadic Hardy-Lorentz space pHra(X) to Lra(X) when X is isomorphic to a p-uniformly smooth space 1 < p ≤ 2). And it is also bounded from Hra(X) to Lra(X) (0 < r < ∝, 0 < a ≤ ∝) hen X has Radon-Nikodym property. In addition, some weak-type inequalities are given.

Key words: Hardy-Lorentz space, dyadic derivative, B-valued martingale, Cesàro mean

CLC Number: 

  • 60G42
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