Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces

Guozhen Lu; Qiaohua Yang

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arXiv · 1703.08171

Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces

Guozhen Lu·Qiaohua Yang

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Abstract

By using, among other things, the Fourier analysis techniques on hyperbolic and symmetric spaces, we establish the Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces. The proof relies on a Hardy-Littlewood-Sobolev inequality on hyperbolic spaces which is of its independent interest. We also give an alternative proof of Benguria, Frank and Loss' work concerning the sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half space. Finally, we show the sharp constant in the Hardy-Sobolev-Maz'ya inequality for bi-Laplacian in the upper half space of dimension five coincides with the Sobolev constant.

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Guozhen Lu, Qiaohua Yang. 2017-03-23. Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces. https://arxiv.org/abs/1703.08171

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