Dimension-independent functional inequalities by tensorization and projection arguments
arxiv(2024)
摘要
We study stability under tensorization and projection-type operations of
gradient-type estimates and other functional inequalities for Markov semigroups
on metric spaces. Using transportation-type inequalities obtained by F. Baudoin
and N. Eldredge in 2021, we prove that constants in the gradient estimates can
be chosen to be independent of the dimension. Our results are applicable to
hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive
diffusions. As a byproduct, we obtain dimension-independent reverse
Poincaré, reverse logarithmic Sobolev, and gradient bounds for Lie groups
with a transverse symmetry and for non-isotropic Heisenberg groups.
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