1. CJM Online first
|Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions|
We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through LSH functions and use it to prove the equivalence of strong hypercontractivity and the strong logarithmic Sobolev inequality for such log-subharmonic functions.
Keywords:logarithmic Sobolev inequalities
2. CJM 2011 (vol 64 pp. 481)
|Some Functional Inequalities on Polynomial Volume Growth Lie Groups|
In this article we study some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended to this general framework without the use of the Littlewood-Paley decomposition.
Keywords:Sobolev inequalities, polynomial volume growth Lie groups