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Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
Nathaniel Eldredge, Leonard Gross, Laurent Saloff-Coste · 2015-10-18 · via math.PR updates on arXiv.org

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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