Exponential-power measures on stratified Lie groups, Grushin and Heisenberg-Greiner spaces satisfy q-super-Poincaré and isoperimetric inequalities with optimal exponent r=(α+1)p/(α+1+αp).
Sharp defective log-Sobolev inequalities on H-type groups
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In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respect to the heat kernel measure. A defective log-Sobolev-type inequality for the Gaussian-like measure with respect to the sub-Riemannian distance is also proved on arbitrary H-type groups.
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2024 1verdicts
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Optimal subelliptic super-Poincar\'e and isoperimetric inequalities on stratified Lie groups
Exponential-power measures on stratified Lie groups, Grushin and Heisenberg-Greiner spaces satisfy q-super-Poincaré and isoperimetric inequalities with optimal exponent r=(α+1)p/(α+1+αp).