2 citations · 2 across the 6 of their papers we have counts for
7 papers
Heat content and spectrum for subordinated sub-Laplacians
Maria Gordina, Liangbing Luo, Andrea Pinamonti +1
We study heat content and spectral properties of subordinated sub-Laplacians on arbitrary Carnot groups. We consider restrictions of such operators to bounded open sets with zero D…
Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs
Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam
Given a complete doubling metric measure space that supports a -Poincaré inequality, we approximate harmonic functions on a bounded domain with a prescribed Newton-Sobol…
Logarithmic Sobolev inequalities on infinite-dimensional reduced Heisenberg groups
Maria Gordina, Liangbing Luo
We construct a family of infinite-dimensional reduced Heisenberg groups which can be viewed as infinite-dimensional homogeneous spaces. Such a space is an analogue of finite-dimens…
Non-Markovian maximal couplings and a vertical reflection principle on a class of sub-Riemannian manifolds
Liangbing Luo, Robert W. Neel
We develop an approach to constructing non-Markovian, non-co-adapted couplings for sub-Riemannian Brownian motions in sub-Riemannian manifolds with large symmetry groups by treatin…
Construction of a Dirichlet form on metric measure spaces of controlled geometry
Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam
Given a compact doubling metric measure space that supports a -Poincaré inequality, we construct a Dirichlet form on that is comparable to the upper gradient en…
Logarithmic Sobolev inequalities on homogeneous spaces
Maria Gordina, Liangbing Luo
We consider sub-Riemannian manifolds which are homogeneous spaces equipped with a natural sub-Riemannian structure induced by a transitive action by a Lie group. In such a setting,…
Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups
Maria Gordina, Liangbing Luo
We study logarithmic Sobolev inequalities with respect to a heat kernel measure on finite-dimensional and infinite-dimensional Heisenberg groups. Such a group is the simplest non-t…