On equivalence of super log Sobolev and Nash type inequalities

• Autorzy: Marco Biroli , Patrick Maheux
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 39B62: Functional inequalities, including subadditivity, convexity, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 2
• Strony: 189-208

Daty

wydano

2014

Twórcy

autor

Marco Biroli

• Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

autor

Patrick Maheux

• Fédération Denis Poisson, (MAPMO, UMR-CNRS 7349), Département de Mathématiques, Université d'Orléans, 45067 Orléans Cedex 2, France

Identyfikatory

DOI

10.4064/cm137-2-4