A1 Journal article (refereed)
Capacities and Density Conditions in Metric Spaces (2024)

Canto, J., Ihnatsyeva, L., Lehrbäck, J., & Vähäkangas, A. V. (2024). Capacities and Density Conditions in Metric Spaces. Potential Analysis, Early online. https://doi.org/10.1007/s11118-024-10137-5

JYU authors or editors

Publication details

All authors or editors: Canto, Javier; Ihnatsyeva, Lizaveta; Lehrbäck, Juha; Vähäkangas, Antti V.

Journal or series: Potential Analysis

ISSN: 0926-2601

eISSN: 1572-929X

Publication year: 2024

Publication date: 30/04/2024

Volume: Early online

Publisher: Springer

Publication country: Netherlands

Publication language: English

DOI: https://doi.org/10.1007/s11118-024-10137-5

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2208.14732

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 (β, p)-capacity and the relative Hajłasz (β, p)-capacity, for 1 < p < ∞ and 0 < β ≤ 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.

Keywords: potential theory; measure theory; metric spaces

Free keywords: comparison of capacities; Riesz capacity; Hajłasz capacity; Hausdorff content; capacity density condition; metric measure space

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2024

Preliminary JUFO rating: 2