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Article Dans Une Revue Semigroup Forum Année : 2015

Super Poincaré and Nash-type inequalities for Subordinated Semigroups

Résumé

We prove that if a super-Poincaré inequality is satisfied by an infinitesimal generator −A of a symmetric contraction semigroup on L2 and that is contracting on L1, then it implies a corresponding super-Poincar ́e inequality for −g(A) for any Bernstein function g. We also study the converse of this statement. We prove similar results for Nash-type inequalities. We apply our results to Euclidean, Riemannian, hypoelliptic and Ornstein- Uhlenbeck settings.
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Dates et versions

hal-00709358 , version 1 (18-06-2012)
hal-00709358 , version 2 (20-10-2014)

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Ivan Gentil, Patrick Maheux. Super Poincaré and Nash-type inequalities for Subordinated Semigroups. Semigroup Forum, 2015, 90 (3), pp.660-693. ⟨10.1007/s00233-014-9648-2⟩. ⟨hal-00709358v2⟩
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