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
收藏
页码：189 / 208
页数：20
相关论文
共 50 条
  • [21] The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces
    Xie, Xiangyun
    Liu, Yu
    Li, Pengtao
    Huang, Jizheng
    ADVANCES IN NONLINEAR ANALYSIS, 2024, 13 (01)
  • [22] Bilinear Sobolev-Poincare, Inequalities and Leibniz-Type Rules
    Bernicot, Frederic
    Maldonado, Diego
    Moen, Kabe
    Naibo, Virginia
    JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (02) : 1144 - 1180
  • [23] On F-Sobolev and Orlicz-Sobolev inequalities
    Kang, Cholryong
    Wang, Fengyu
    FRONTIERS OF MATHEMATICS IN CHINA, 2009, 4 (04) : 659 - 667
  • [24] On F-Sobolev and Orlicz-Sobolev inequalities
    Cholryong Kang
    Fengyu Wang
    Frontiers of Mathematics in China, 2009, 4 : 659 - 667
  • [25] Sobolev-type inequalities and heat kernel bounds along the geometric flow
    Abolarinwa, Abimbola
    AFRIKA MATEMATIKA, 2016, 27 (1-2) : 169 - 186
  • [26] Sobolev-type inequalities for potentials in grand variable exponent Lebesgue spaces
    Edmunds, David E.
    Kokilashvili, Vakhtang
    Meskhi, Alexander
    MATHEMATISCHE NACHRICHTEN, 2019, 292 (10) : 2174 - 2188
  • [27] SOBOLEV AND TRUDINGER TYPE INEQUALITIES ON GRAND MUSIELAK-ORLICZ-MORREY SPACES
    Maeda, Fumi-Yuki
    Mizuta, Yoshihiro
    Ohno, Takao
    Shimomura, Tetsu
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2015, 40 (01) : 403 - 426
  • [28] Monotonicity of the Extremal Functions for One-dimensional Inequalities of Logarithmic Sobolev Type
    Miclo, Laurent
    SEMINAIRE DE PROBABILITES XLII, 2009, 1979 : 103 - 130
  • [29] Sobolev type inequalities for fractional maximal functions and Green potentials in half spaces
    Mizuta, Yoshihiro
    Shimomura, Tetsu
    POSITIVITY, 2021, 25 (03) : 1131 - 1146
  • [30] Logarithmic Sobolev Inequalities for Infinite Dimensional Hormander Type Generators on the Heisenberg Group
    Inglis, J.
    Papageorgiou, I.
    POTENTIAL ANALYSIS, 2009, 31 (01) : 79 - 102
12345