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

共 50 条

[21] Super-Poincaré and Nash-type inequalities for subordinated semigroups
Ivan Gentil
Patrick Maheux
Semigroup Forum, 2015, 90 : 660 - 693
[22] Poincare and Log-Sobolev Inequalities for Mixtures
Schlichting, Andre
ENTROPY, 2019, 21 (01):
[23] A generalization of poincaré and log-Sobolev inequalities
Wang F.-Y.
Potential Analysis, 2005, 22 (1) : 1 - 15
[24] Fractional Log-Sobolev Inequalities on the SphereFractional Log-Sobolev Inequalities...H. Tang, C. Zhang
Hanli Tang
Caifeng Zhang
The Journal of Geometric Analysis, 2025, 35 (5):
[25] Relative Nash-Type and L2-Sobolev Inequalities in Dunkl Setting
Mustapha, Sami
Sifi, Mohamed
COMPLEX ANALYSIS AND OPERATOR THEORY, 2021, 15 (08)
[26] Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
Adamczak, Radoslaw
Polaczyk, Bartlomiej
Strzelecki, Michal
JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 282 (07)
[27] Log-Sobolev-type inequalities for solutions to stationary Fokker–Planck–Kolmogorov equations
V. I. Bogachev
A. V. Shaposhnikov
S. V. Shaposhnikov
Calculus of Variations and Partial Differential Equations, 2019, 58
[28] Quantum Gaussian maximizers and log-Sobolev inequalities
Holevo, Alexander S.
Filippov, Sergey N.
LETTERS IN MATHEMATICAL PHYSICS, 2023, 113 (01)
[29] ON LOG-SOBOLEV INEQUALITIES FOR INFINITE LATTICE SYSTEMS
ZEGARLINSKI, B
LETTERS IN MATHEMATICAL PHYSICS, 1990, 20 (03) : 173 - 182
[30] Equivalence of analytic and Sobolev Poincare inequalities for planar domains
Stanoyevitch, A
Stegenga, DA
PACIFIC JOURNAL OF MATHEMATICS, 1997, 178 (02) : 363 - 375

← 1 2 3 4 5 →