THE DYADIC DERIVATIVE AND CESARO MEAN OF BANACH-VALUED MARTINGALES

THE DYADIC DERIVATIVE AND CESARO MEAN OF BANACH-VALUED MARTINGALES

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 derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic...

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Veröffentlicht in:Acta mathematica scientia 2009-03, Vol.29 (2), p.265-275
1. Verfasser: 陈丽红 刘培德
Format: Artikel
Sprache:eng
Schlagworte:
43A17
60G42
B-valued martingale
Banach空间
Cesàro mean
dyadic derivative
Hardy
Hardy-Lorentz space
Radon
一致光滑空间
洛伦兹空间
衍生物
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Zusammenfassung: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 derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（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≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(09)60027-8