SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.

作 者：   作者單位：   刊 名： 數學年刊B輯（英文版）  ISTIC SCI 英文刊名： CHINESE ANNALS OF MATHEMATICS,SERIES B  年，卷(期)： 2005 26(4)  分類號： O1  關鍵詞： Sobolev inequality   Complete manifold   Riesz transform   Potential   Heat kernel  

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