The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces

被引：3

作者：

Lierl, Janna ^{[1
]}

机构：

[1] Tech Univ Clausthal, Inst Math, Erzstr 1, D-38678 Clausthal Zellerfeld, Germany

来源：

POTENTIAL ANALYSIS | 2022年 / 57卷 / 04期

关键词：

Dirichlet heat kernel; Fractals; h-transform; Inner uniform domains; Ultracontractivity; Harnack inequality; BOUNDARY HARNACK PRINCIPLE; BROWNIAN-MOTION; TRANSITION DENSITIES; MARTIN BOUNDARY; ULTRACONTRACTIVITY; INEQUALITIES; STABILITY;

D O I：

10.1007/s11118-021-09926-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper proves two-sided estimates for the Dirichlet heat kernel on inner uniform domains in metric measure Dirichlet spaces satisfying the volume doubling condition, the Poincare inequality, and a cutoff Sobolev inequality. More generally, we obtain local upper and lower bounds for the Dirichlet heat kernel on locally inner uniform domains under local geometric assumptions on the underlying space.

引用

页码：521 / 543

页数：23

共 49 条

[1] The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces
Janna Lierl
[J]. Potential Analysis, 2022, 57 : 521 - 543
[2] Publisher Correction: The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces
Janna Lierl
[J]. Potential Analysis, 2024, 60 (1) : 553 - 554
[3] The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces (Jun, 10.1007/s11118-021-09926-z, 2021)
Lierl, Janna
[J]. POTENTIAL ANALYSIS, 2024, 60 (01) : 553 - 554
[4] Scale-invariant Boundary Harnack Principle on Inner Uniform Domains in Fractal-type Spaces
Janna Lierl
[J]. Potential Analysis, 2015, 43 : 717 - 747
[5] Scale-invariant Boundary Harnack Principle on Inner Uniform Domains in Fractal-type Spaces
Lierl, Janna
[J]. POTENTIAL ANALYSIS, 2015, 43 (04) : 717 - 747
[6] Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces
Lierl, Janna
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2018, 34 (02) : 687 - 738
[7] NEUMANN AND DIRICHLET HEAT KERNELS IN INNER UNIFORM DOMAINS
Gyrya, Pavel
Saloff-Coste, Laurent
[J]. ASTERISQUE, 2011, (336) : 1 - +
[8] The Dirichlet heat kernel in inner uniform domains: Local results, compact domains and non-symmetric forms
Lierl, Janna
Saloff-Coste, Laurent
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (07) : 4189 - 4235
[9] Inner function in Dirichlet type spaces
Qian, Ruishen
Shi, Yecheng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 421 (02) : 1844 - 1854
[10] On the subinvariance of inner uniform domains in Banach spaces
Hu, Caicai
He, Yuehui
[J]. JOURNAL OF ANALYSIS, 2024, 32 (03): : 1773 - 1785

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