English

Classifying Triebel-Lizorkin capacities in metric spaces

Classical Analysis and ODEs 2024-03-20 v1 Analysis of PDEs

Abstract

We study non-local or fractional capacities in metric measure spaces. Our main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin capacities, potentional Triebel-Lizorkin capacities, and metric space variants of Riesz capacities. As an application of our results, we obtain a characterization of a Hajlasz-Triebel-Lizorkin capacity density condition, which is based on an earlier characterization of a Riesz capacity density condition in terms of Hausdorff contents.

Keywords

Cite

@article{arxiv.2403.12513,
  title  = {Classifying Triebel-Lizorkin capacities in metric spaces},
  author = {Juha Lehrbäck and Kaushik Mohanta and Antti V. Vähäkangas},
  journal= {arXiv preprint arXiv:2403.12513},
  year   = {2024}
}