ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIES (old title: Super Logarithmic Sobolev inequalities and Nash-type inequalities for sub-markovian symmetric semigroups)
Résumé
We prove the equivalence of Nash type and super logSobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence be- tween super log Sobolev or Nash type inequalities and ultracontractiv- ity. We discuss Davies-Simon’s counterexample as borderline case of this equivalence and related open problems.
Origine | Fichiers produits par l'(les) auteur(s) |
---|