On first order interpolation inequalities with weights on the Heisenberg group |
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| Authors: | Ya Zhou Han Peng Cheng Niu Shu Tao Zhang |
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| Institution: | (1) School of Mathematics and Statistics, Xiaogan University, Xiaogan, Hubei, 432000, People’s Republic of China |
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| Abstract: | In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg
group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of
Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,
we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined. |
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| Keywords: | Interpolation inequality Hardy-Sobolev type inequality Hardy type inequality Heisenberg group |
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