Acta mathematica scientia, Series B >
BOUNDEDNESS OF DYADIC DERIVATIVE AND CESÀRO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES
Received date: 2008-10-16
Online 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)
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 p∑α, 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
CHEN Li-Hong , LIU Pei-De . BOUNDEDNESS OF DYADIC DERIVATIVE AND CESÀRO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 268 -280 . DOI: 10.1016/S0252-9602(11)60227-0
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