Capacities and Density Conditions in Metric Spaces

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-04-30 DOI:10.1007/s11118-024-10137-5

Javier Canto, Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas

引用次数: 0

Abstract

We examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz \((\beta ,p)\)-capacity and the relative Hajłasz \((\beta ,p)\)-capacity, for \(1<p<\infty \) and \(0<\beta \le 1\), under a suitable kernel estimate related to the Riesz potential. Then we show that in geodesic spaces the corresponding capacity density conditions are equivalent even without assuming the kernel estimate. In the last part of the paper, we compare the relative Hajłasz (1, p)-capacity to the relative variational p-capacity.

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公制空间中的容量和密度条件

我们研究了在度量空间中不同容量之间的关系。首先，我们证明了在（1<p<infty \）和（0<beta \le 1\）下，在与Riesz势相关的合适的核估计下，Riesz \（（beta ,p））-容量和相对Hajłasz \（（beta ,p））-容量的可比性结果。然后我们证明，在测地空间中，即使不假设核估计，相应的容量密度条件也是等价的。在本文的最后一部分，我们将相对 Hajłasz (1, p) 容量与相对变分 p 容量进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.