Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere

• 成果类型: Article
• 署名作者: Branson, Thomas P.; Fontana, Luigi; Morpurgo, Carlo
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/anals.2013.177.1.1
• 发表日期: 2013
• 页码: 1-52
• 关键词: zeta-function determinants; hardy-littlewood-sobolev; sharp constants; intertwining-operators; fundamental solution; invariant powers; extremal metrics; laplacian; SPACES; CURVATURE

摘要

We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CR-pluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequality in the form given by Carlen and Loss.