Geodesic
Moser-Trudinger and Beckner-Onofri’s inequalities on the CR sphere
Thomas P. Branson   ; Luigi Fontana 1   ; Carlo Morpurgo 2
1 Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, 20125 Milano, Italy
2 Mathematics Department, University of Missouri, Columbia, MO 65211
Annals of mathematics, Tome 177 (2013) no. 1, pp. 1-52 Cet article a éte moissonné depuis la source Annals of Mathematics website

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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.

DOI : 10.4007/annals.2013.177.1.1

Thomas P. Branson    ; Luigi Fontana  1   ; Carlo Morpurgo  2

1 Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, 20125 Milano, Italy
2 Mathematics Department, University of Missouri, Columbia, MO 65211 
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Thomas P. Branson; Luigi Fontana; Carlo Morpurgo. Moser-Trudinger and Beckner-Onofri’s inequalities on the CR sphere. Annals of mathematics, Tome 177 (2013) no. 1, pp. 1-52. doi: 10.4007/annals.2013.177.1.1

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