ON EQUIVALENCE OF SUPER LOG SOBOLEV AND NASH TYPE INEQUALITIES

被引：0

作者：

Biroli, Marco ^{[1
]}

Maheux, Patrick ^{[2
]}

机构：

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Univ Orleans, Federat Denis Poisson, MAPMO, Dept Math,UMR CNRS 7349, F-45067 Orleans 2, France

来源：

COLLOQUIUM MATHEMATICUM | 2014年 / 137卷 / 02期

关键词：

ultracontractivity; super log Sobolev inequality; Nash type inequality; Orlicz-Sobolev inequality; semigroups of operators; Dirichlet form; heat kernel; infinite-dimensional torus; HEAT KERNELS; UPPER-BOUNDS; ULTRACONTRACTIVITY; OPERATORS;

D O I：

10.4064/cm137-2-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：189 / 208

页数：20

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