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


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.


Thomas P. Branson

Luigi Fontana

Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, 20125 Milano, Italy

Carlo Morpurgo

Mathematics Department, University of Missouri, Columbia, MO 65211