Acta mathematica scientia, Series B >
THE DYADIC DERIVATIVE AND CESÀRO MEAN OF BANACH-VALUED MARTINGALES
Received date: 2006-09-17
Online published: 2009-03-20
Supported by
This work was supported by the National Natural Science Foundation of China (10371093)
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
CHEN Li-Gong , LIU Pei-De . THE DYADIC DERIVATIVE AND CESÀRO MEAN OF BANACH-VALUED MARTINGALES[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 265 -275 . DOI: 10.1016/S0252-9602(09)60027-8
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