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We derive sharp Moser-Trudinger inequalities on the CR sphere. The first typeis in the Adams form, for powers of the sublaplacian and for general spectrallydefined operators on the space of CR-pluriharmonic functions. We will thenobtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions onthe sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolevinequality in the form given by Carlen and Loss.

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