洛伦兹空间上的分布函数的极限性质 |
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作者姓名: | 吴迪 邓杨肯迪 于丹丹 燕敦验 |
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作者单位: | 1. 浙江科技学院理学院, 杭州 310023;2. 中国科学院大学数学科学学院, 北京 100049 |
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基金项目: | NSF of Zhejiang Province of China (LQ18A010002,LQ17A010002) |
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摘 要: | 用一个新颖的方法证明以下等式:$\mathop {\lim }\limits_{\alpha \to {0^ + }} {\alpha ^P}{d_f}(\alpha ) = \mathop {\lim }\limits_{\alpha \to \infty } {\alpha ^P}{d_f}(\alpha ) = 0$其中 f∈Lp,q(X,μ),并且有0<p<∞和0<q<∞。也证明函数αp在某种意义下不能再提升。特别地,当q=∞时,以上等式是不一定成立的。
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关 键 词: | 极限行为 分布函数 洛伦兹空间 |
收稿时间: | 2021-01-05 |
修稿时间: | 2021-03-03 |
Limiting property of distribution function in Lorentz space |
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Authors: | WU Di DENG Yangkendi YU Dandan YAN Dunyan |
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Institution: | 1. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | In this paper, we give a novel proof for the following equality$\mathop {\lim }\limits_{\alpha \to {0^ + }} {\alpha ^P}{d_f}(\alpha ) = \mathop {\lim }\limits_{\alpha \to \infty } {\alpha ^P}{d_f}(\alpha ) = 0$for f∈Lp,q(X,μ) with 0<p<∞, and 0<q<∞.We also prove that the function αp can not be improved for some sense. When q=∞, the above equality does not hold. |
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Keywords: | limiting behavior distribution functions Lorentz spaces |
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