An Extension of Hardy-Littlewood-Sobolev Inequality

An Extension of Hardy-Littlewood-Sobolev Inequality

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Meijun Zhu, University of Oklahoma
Fine Hall 314

The classical Hardy-Littlewood-Sobolev inequality implies Sobolev and other geometric inequalities and has a great impact to geometric analysis. Recent results on Sobolev inequalities with negative power indicate the existence of certain extensions to the classical HLS inequality. In this talk, we shall reveal one extension. The existence of sharp constant, as well as the classification of certain extremal functions via the method of moving sphere are also obtained. This is a joint work with J. Dou.