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

Abstract

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.

53 Pages. Several minor corrections and changes in v5. Pages 22-24 are revised. Section 2 is condensed and some proofs are omitted (but can still be found in v3). Some references are added. To appear in Annals of Mathematics

References in corpus (1)

• Extremals for Logarithmic Hardy-Littlewood-Sobolev inequalities on compact manifolds

Cited by in corpus (6)

• Sharp constants in several inequalities on the Heisenberg group
• The Subelliptic Heat Kernel on the CR sphere
• Moser-Trudinger inequality on conformal discs
• The Research of Thomas P. Branson
• Sharp Moser-Trudinger inequalities for the Laplacian without boundary conditions
• Adams inequalities on measure spaces