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Strong hypercontractivity and strong logarithmic Sobolev inequalities on stratified Lie groups. (arXiv:1706.07517v1 [math.FA])
来源于:arXiv
On a stratified Lie group $G$ equipped with hypoelliptic heat kernel measure,
we study the behavior of the dilation semigroup on $L^p$ spaces of
log-subharmonic functions. We consider a notion of strong hypercontractivity
and a strong logarithmic Sobolev inequality, and show that these properties are
equivalent for any group $G$. Moreover, if $G$ satisfies a classical
logarithmic Sobolev inequality, then both properties hold. This extends similar
results obtained by Graczyk, Kemp and Loeb in the Euclidean setting. 查看全文>>