Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups

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.

46 pages. Minor corrections. To appear in Transactions of the American Mathematical Society

References in corpus (3)

• On gradient bounds for the heat kernel on the Heisenberg group
• Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups
• Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions

Cited by in corpus (2)

• Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups
• Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups