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ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIES

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00465177
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Submitted on : Thursday, November 20, 2014 - 4:58:38 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:12 PM
Long-term archiving on: : Monday, February 23, 2015 - 8:51:02 AM

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Marco Biroli, Patrick Maheux. ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIES. Colloquium Mathematicum, 2014, 137 (2), pp.189-208. ⟨10.4064/cm137-2-4⟩. ⟨hal-00465177v3⟩

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