Acta mathematica scientia, Series B >
TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES
Received date: 2011-03-21
Revised date: 2011-11-25
Online published: 2013-01-20
Supported by
This work was supported by National Natural Science Foundation of China (11201354), Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201121), National Natural Science Foundation of Pre-Research Project (2011XG005) and also supported by Natural Science Fund of Hubei Province (2010CDB03305), Wuhan Chenguang Program (201150431096), Open Fund of State Key Laboratory of Information Engineering in Surveying Mapping and Remote Sensing (11R01).
In [1] the boundedness of one dimensional maximal operator of dyadic deriva-tive is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space Hq to the Hardy space Hq for 0 < q ≤ 1 and is bounded from p∑α , Dα to Lα for some α.
Key words： Hardy space; dyadic derivative; dyadic integral
ZHANG Chuan-Zhou , ZHANG Xue-Ying . TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES[J]. Acta mathematica scientia, Series B, 2013 , 33(1) : 279 -289 . DOI: 10.1016/S0252-9602(12)60210-0
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