中国科学院大学学报2019，Vol.36Issue(5)：577-580,4.DOI:10.7523/j.issn.2095-6134.2019.05.001
限制在闭超曲面上的卷积
Convolution integral restricted on closed hypersurfaces
摘要
Abstract
The classical convolution integral on Euclidean space is given as follows.For f ∈L1(R n) andg ∈ Lp(R n),Tf(g)is defined as Tf(g) (x):=f* g(x) =∫Rf(x-y)g(y)dy.It has many applications in analysis and engineering.Young's inequality demonstrates that Tf:Lp(R n) →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.关键词
卷积/闭超曲面/有界性Key words
convolution integral/closed hypersurface/boundedness分类
数理科学引用本文复制引用
杜文奎,燕敦验..限制在闭超曲面上的卷积[J].中国科学院大学学报,2019,36(5):577-580,4.基金项目
Supported by the National Nature Science Foundation of China (11471309,11561062) （11471309,11561062）
