Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn

W Beckner

doi:10.1073/pnas.89.11.4816

Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn

Proc Natl Acad Sci U S A. 1992 Jun 1;89(11):4816-9. doi: 10.1073/pnas.89.11.4816.

Author

W Beckner¹

Affiliation

¹ Department of Mathematics, University of Texas, Austin, TX 78712, USA.

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.