Poisson transforms for real rank one semisimple Lie groups have sharp boundedness and closed-range properties from Sobolev spaces to L2 spaces, with compact commutators, proving the remaining open part of Julg's conjecture on the Baum-Connes conjecture.
Melin,Lie filtrations and pseudo-differential operators, Preprint, 1982
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Sharp mapping properties of Poisson transforms and the Baum-Connes conjecture
Poisson transforms for real rank one semisimple Lie groups have sharp boundedness and closed-range properties from Sobolev spaces to L2 spaces, with compact commutators, proving the remaining open part of Julg's conjecture on the Baum-Connes conjecture.