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arXiv · 2403.12513

Classifying Triebel-Lizorkin capacities in metric spaces

Juha Lehrbäck·Kaushik Mohanta·Antti V. Vähäkangas
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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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Juha Lehrbäck, Kaushik Mohanta, Antti V. Vähäkangas. 2024-03-19. Classifying Triebel-Lizorkin capacities in metric spaces. https://arxiv.org/abs/2403.12513

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