关键词: 卷积, 闭超曲面, 有界性

Abstract: The classical convolution integral on Euclidean space is given as follows. For f∈L¹(Rⁿ) and g∈L^p(Rⁿ), T_f(g) is defined as
T_f(g)(x):f*g(x)=∫_Rⁿf(x-y)g(y)dy.
It has many applications in analysis and engineering. Young's inequality demonstrates that T_f:L^p(Rⁿ)→L^p(Rⁿ) is a bounded operator for 1 ≤ p ≤ ∞. In this study, we have obtained the estimation of the L^p norm of convolution integral restricted on closed hypersurfaces. More precisely, we have established Young's inequality on closed hypersurfaces.

Key words: convolution integral, closed hypersurface, boundedness