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. Peloso
Secondo
;
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.
Settore MAT/05 - Analisi Matematica
4-giu-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/933446
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