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

2017/03/23 by Guozhen Lu, Lu, Guozhen, Qiaohua Yang +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.08171

openalex publication_date 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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