Hardy-Sobolev type inequalities on the H-type group |
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| Authors: | Yazhou Han Pengcheng Niu |
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| Institution: | (1) Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710072, P.R.China;(2) Present address: Department of Mathematics, College of Science, China Jiliang University, 310018, P.R. China |
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| Abstract: | Motivated by the idea of Badiale and Tarantello who have found Hardy-Sobolev inequalities on Rn, a class of Hardy-Sobolev type inequalities on H-type groups is proved via a new representation formula for functions. Extremal
functions realizing equality in the inequalities are discussed by refined Concentration-Compactness principles. Finally, some
sharp constants for Hardy type inequalities are given.
The project supported by National Natural Science Foundation of China, Grant No. 10371099. |
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| Keywords: | 22E30 35H20 |
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