Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
نویسنده
چکیده
We show that for a hypoelliptic Dirichlet form operatorA 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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