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Super Poincaré and Nash-type inequalities for Subordinated Semigroups

Abstract : 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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Submitted on : Monday, October 20, 2014 - 5:44:34 PM
Last modification on : Thursday, April 16, 2020 - 12:19:51 PM
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Ivan Gentil, Patrick Maheux. Super Poincaré and Nash-type inequalities for Subordinated Semigroups. Semigroup Forum, Springer Verlag, 2015, 90 (3), pp.660-693. ⟨10.1007/s00233-014-9648-2⟩. ⟨hal-00709358v2⟩

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