We prove a local (Formula presented.) -Poincaré inequality, (Formula presented.), on non-compact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and that if the group is non-doubling, then its growth is indeed, in general, exponential. We also prove a non-local (Formula presented.) -Poincaré inequality with respect to suitable finite measures on the group.
Local and non-local Poincaré inequalities on Lie groups
Bruno T.;Peloso M. M.;
2022-01-01
Abstract
We prove a local (Formula presented.) -Poincaré inequality, (Formula presented.), on non-compact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and that if the group is non-doubling, then its growth is indeed, in general, exponential. We also prove a non-local (Formula presented.) -Poincaré inequality with respect to suitable finite measures on the group.
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