| Littlewood–Paley Operators on Spaces with Variable Exponent on Homogeneous Groups |
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| 作者姓名： | Dong Li LIU Ji Man ZHAO |
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| 作者单位： | Key Laboratory of Mathematics and Complex Systems |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11471040 and 11761131002) |
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| 摘 要： | In this paper,on homogeneous groups,we study the Littlewood–Paley operators in variable exponent spaces.First,we prove that the weighted Littlewood–Paley operators are controlled by the weighted Hardy–Littlewood maximal function,and obtain the vector-valued inequalities of the Littlewood–Paley operators,including the Lusin function,Littlewood–Paley g function and gλ* function.Second,we prove the boundedness of multilinear Littlewood–Paley gψ,λ* function.
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| 关 键 词： | Littlewood–Paley OPERATORS variable LEBESGUE SPACES HOMOGENEOUS groups |
Littlewood-Paley Operators on Spaces with Variable Exponent on Homogeneous Groups |
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| Dong Li LIU,Ji Man ZHAO.Littlewood-Paley Operators on Spaces with Variable Exponent on Homogeneous Groups[J].Acta Mathematica Sinica,2020,36(5):535-558. |
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| Authors: | Liu Dong Li Zhao Ji Man |
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| Institution: | Key Laboratory of Mathematics and Complex Systems, Ministry of Education Institution of Mathematics and Mathematical Education School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | In this paper, on homogeneous groups, we study the Littlewood-Paley operators in variable exponent spaces. First, we prove that the weighted Littlewood-Paley operators are controlled by the weighted Hardy-Littlewood maximal function, and obtain the vector-valued inequalities of the Littlewood-Paley operators, including the Lusin function, Littlewood-Paley g function and gλ* function. Second, we prove the boundedness of multilinear Littlewood-Paley gψ,λ* function. |
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| Keywords: | Littlewood-Paley operators variable Lebesgue spaces homogeneous groups |
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