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.
DU Wenkui
,
YAN Dunyan
. Convolution integral restricted on closed hypersurfaces[J]. Journal of University of Chinese Academy of Sciences, 2019
, 36(5)
: 577
-580
.
DOI: 10.7523/j.issn.2095-6134.2019.05.001
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