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

1 June 1992

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America

Vol. 89 (11), 4816-4819
https://doi.org/10.1073/pnas.89.11.4816

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.

Keywords

FUNCTION
INEQUALITY
SOBOLEV INEQUALITIES
POISSON SEMIGROUP
ENTROPY

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