We prove a local (Formula presented. Lp$L<^>p$-Poincare inequality, 1 <= p2$-) -Poincaré inequality on non-compact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and that if the group is non-doubling, then its growth is indeed, in general, exponential. We also prove a non-local (Formula presented.) -Poincaré inequality with respect to suitable finite measures on the group.
Local and non-local Poincare inequalities on Lie groups / T. Bruno, M. Peloso, M. Vallarino. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 54:6(2022 Dec), pp. 2162-2173. [10.1112/blms.12684]
Local and non-local Poincare inequalities on Lie groups
M. PelosoSecondo
;
2022
Abstract
We prove a local (Formula presented. Lp$L<^>p$-Poincare inequality, 1 <= p2$-) -Poincaré inequality 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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