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arXiv · 1510.05151

Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups

Nathaniel Eldredge·Leonard Gross·Laurent Saloff-Coste
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Abstract

We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is strongly hypercontractive in the sense of Janson. This extends previous results of Gross to a setting in which the operator A is not holomorphic.

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Nathaniel Eldredge, Leonard Gross, Laurent Saloff-Coste. 2017-09-13. Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups. https://doi.org/10.1090/tran%2F7200

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