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Classifying Triebel-Lizorkin capacities in metric spaces

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arxiv 2403.12513 v1 pith:23RHKPQN submitted 2024-03-19 math.CA math.AP

Juha Lehrbäck , Kaushik Mohanta , Antti V. Vähäkangas This is my paper · ORCID
classification math.CAmath.AP
keywords capacitiesmetriccapacitycharacterizationconditiondensityhajlasz-triebel-lizorkinriesz
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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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  1. Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

    math.AP 2024-12 conditional novelty 8.0 of 10

    Fractional Hardy inequalities in doubling metric measure spaces self-improve in both the power p and the regularity theta, via an equivalence with Hardy inequalities in hyperbolic fillings.

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