Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces |
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Authors: | Xingsong ZHANG Mingquan WEI Dunyan YAN Qianjun HE |
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Affiliation: | 1. School of Mathematics, University of Chinese Academy of Sciences, Beijing 100049, China2. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China3. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China |
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Abstract: | We will prove that for and , the central Morrey norm of the truncated centered Hardy-Littlewood maximal operator equals that of the centered Hardy-Littlewood maximal operator for all . When p = 1 and , it turns out that the weak central Morrey norm of the truncated centered Hardy-Littlewood maximal operator equals that of the centered Hardy-Littlewood maximal operator for all . Moreover, the same results are true for the truncated uncentered Hardy-Littlewood maximal operator. Our work extends the previous results of Lebesgue spaces to Morrey spaces. |
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Keywords: | Hardy-Littlewood maximal function truncated Hardy-Littlewood maximal function Morrey norms weak Morrey norms |
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