Classifying Triebel-Lizorkin capacities in metric spaces

2024/03/19 by Juha Lehrbäck, Lehrbäck, Juha, Kaushik Mohanta +3 · 1 citation
Mathematics · #31C15 (28A12 #31E05) #Advanced Topology and Set Theory #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2403.12513

openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Limits at infinity for Hajłasz-Sobolev functions in metric spaces

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