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.

Branson, T., Fontana, L., Morpurgo, C. (2007). Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere.

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

FONTANA, LUIGI;
2007

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.
Scientifica
Sharp inequalities, CR-sphere, Heisenberg group, Intertwining Operators, conformal invariance
English
arXiv: 0712.3905v1[math.AP] 23 Dec 2007
Si tratta del preprint di un lavoro sottopostoper la pubblicazione ad "Annals of Mathematics" nel settembre del 2007 e ancora in attesa del responso del referee.
Branson, T., Fontana, L., Morpurgo, C. (2007). Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere.
Branson, T; Fontana, L; Morpurgo, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/8591
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