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。
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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