Geodesic
On equivalence of super log Sobolev and Nash type inequalities
Marco Biroli 1   ; Patrick Maheux 2
1 Dipartimento di Matematica “F. Brioschi” Politecnico di Milano Piazza Leonardo da Vinci 32 20133, Milano, Italy
2 Fédération Denis Poisson (MAPMO, UMR-CNRS 7349) Département de Mathématiques Université d'Orléans 45067 Orléans Cedex 2, France
Colloquium Mathematicum, Tome 137 (2014) no. 2, pp. 189-208 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove the equivalence of Nash type and super log Sobolev 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 between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies–Simon's counterexample as the borderline case of this equivalence and related open problems.
DOI : 10.4064/cm137-2-4
Keywords: prove equivalence nash type super log sobolev inequalities dirichlet forms inequalities equivalent orlicz sobolev type inequalities ultracontractivity semigroup assumed known there equivalence between super log sobolev nash type inequalities ultracontractivity discuss davies simons counterexample borderline equivalence related problems

Marco Biroli  1   ; Patrick Maheux  2

1 Dipartimento di Matematica “F. Brioschi” Politecnico di Milano Piazza Leonardo da Vinci 32 20133, Milano, Italy
2 Fédération Denis Poisson (MAPMO, UMR-CNRS 7349) Département de Mathématiques Université d'Orléans 45067 Orléans Cedex 2, France 
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     title = {On equivalence of super log {Sobolev} and
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 Nash type inequalities
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Marco Biroli; Patrick Maheux. On equivalence of super log Sobolev and
 Nash type inequalities. Colloquium Mathematicum, Tome 137 (2014) no. 2, pp. 189-208. doi: 10.4064/cm137-2-4

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