限制在闭超曲面上的卷积 |
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作者姓名: | 杜文奎 燕敦验 |
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作者单位: | 中国科学院大学数学科学学院, 北京 100049 |
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基金项目: | Supported by the National Nature Science Foundation of China (11471309,11561062) |
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摘 要: | 经典的欧氏空间中的卷积如下给出。对f∈L1(Rn)和g∈Lp(Rn),
Tf(g)(x)∶f*g(x)=∫Rnf(x-y)g(y)dy.
这样的卷积在分析、物理和工程上都有广泛的应用。经典的Young不等式表明,对1≤p≤∞,Tf:Lp(Rn)→Lp(Rn)是有界线性算子。得到限制在一个闭超曲面(欧氏空间中的余维数为1的紧致无边连通正则子流形)上的卷积的Lp模估计的大小。更精确地说,把Young不等式推广到了闭超曲面上。
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关 键 词: | 卷积 闭超曲面 有界性 |
收稿时间: | 2018-04-13 |
修稿时间: | 2018-04-27 |
Convolution integral restricted on closed hypersurfaces |
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Authors: | DU Wenkui YAN Dunyan |
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Institution: | College of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | The classical convolution integral on Euclidean space is given as follows. For f∈L1(Rn) and g∈Lp(Rn), Tf(g) is defined as
Tf(g)(x):f*g(x)=∫Rnf(x-y)g(y)dy.
It has many applications in analysis and engineering. Young's inequality demonstrates that Tf:Lp(Rn)→Lp(Rn) is a bounded operator for 1 ≤ p ≤ ∞. In this study, we have obtained the estimation of the Lp norm of convolution integral restricted on closed hypersurfaces. More precisely, we have established Young's inequality on closed hypersurfaces. |
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Keywords: | convolution integral closed hypersurface boundedness |
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