On equivalence of super log Sobolev and Nash type inequalities
| Autor: | Marco Biroli, Patrick Maheux |
|---|---|
| Přispěvatelé: | Dipartimento di Matematica (DIPARTIMENTO DI MATEMATICA), Politecnico di Milano [Milan] (POLIMI), Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO) |
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Inequality Semigroup General Mathematics media_common.quotation_subject Mathematics::Analysis of PDEs Orlicz-Sobolev inequality Mathematics::Spectral Theory Type (model theory) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] Dirichlet distribution Sobolev inequality Sobolev space symbols.namesake symbols Logarithmic Sobolev inequalities Equivalence (measure theory) Nash-type inequality sub-markovian semigroup 39B62 Counterexample Mathematics media_common |
| Zdroj: | Colloquium Mathematicum Colloquium Mathematicum, 2014, 137 (2), pp.189-208. ⟨10.4064/cm137-2-4⟩ |
| ISSN: | 1730-6302 0010-1354 |
| DOI: | 10.4064/cm137-2-4 |
| Popis: | Several years ago, a French version was available but with a limited diffusion.Here is the final version to appear in Colloquium Mathematicum.(Theorem 4.1 statement (2) corrected); International audience; 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. |
| Databáze: | OpenAIRE |
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