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

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

2007-12-23

arxiv.org/abs/0712.3905v3

Mathematics

Analysis of PDEs

64 Pages. Minor corrections and changes in v2. Statement of Thm. 2.2 and proof of Lemma 2.3 corrected in v3

Scientific paper

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.

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