ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIESReport as inadecuate




ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIES - Download this document for free, or read online. Document in PDF available to download.

* Corresponding author 1 DIPARTIMENTO DI MATEMATICA - Dipartimento di Matematica 2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Keywords : Orlicz-Sobolev inequality sub-markovian semigroup Nash-type inequality Logarithmic Sobolev inequalities





Author: Marco Biroli - Patrick Maheux -

Source: https://hal.archives-ouvertes.fr/



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