title: Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
abstract: Hypercontractive estimates are obtained for the Poisson semigroup on Lp(Sn). Such estimates are determined by a sharp logarithmic Sobolev inequality that relates the entropy of a function on Sn to its smoothness.
authors.affiliation: Department of Mathematics, University of Texas, Austin, TX 78712, USA.
authors.forename: W
authors.initials: W
authors.lastname: Beckner