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| SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS |
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Citation： |
WANG Meng.SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS[J].Chinese Annals of Mathematics B,2005,26(4):651~658 |
| Page view： 1096
Net amount： 801 |
Authors： |
WANG Meng; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271107), the 973 Project of the Ministry of Science and Technology of China (No.G1999075105) and the Zhejiang Provincial Natural Science Foundation of China (No.RC97017). |
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| Abstract： |
Let M be an n dimensional complete Riemannian manifold satisfying the doubling volume property and an on-diagonal heat kernel estimate. The necessary-sufficient condition for the Sobolev inequality $\|f\|_{q}\le C_{n,,\nu,p,q}(\|\nabla f\|_{p}+\|f\|_{p})\ (2\le p |
Keywords： |
Sobolev inequality, Complete manifold, Riesz transform, Potential, Heat kernel |
Classification： |
46E35, 53C25 |
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