TWO-DIMENSIONAL MAXIMAL OPERATOR OF DYADIC DERIVATIVE ON VILENKIN MARTINGALE SPACES |
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| Authors: | Chuanzhou ZHANG Xueying ZHANG |
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| Institution: | 1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology), Wuhan 430081, China |
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| Abstract: | In 1] the boundedness of one dimensional maximal operator of dyadic derivative 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 pΣα, Dα to Lα for some α. |
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| Keywords: | Hardy space dyadic derivative dyadic integral |
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