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arXiv · 2312.08297

On a quasi-additivity formula for the capacity on Ahlfors-regular spaces

Michelangelo Cavina
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Abstract

In this work we prove formulas of quasi-additivity for the capacity associated to kernels of radial type in the setting of the boundary of a tree structure and in the setting of compact Ahlfors-regular spaces. We also define a notion of harmonic extension, to one additional variable, of a function defined over a compact Ahlfors-regular space, and we prove a result of tangential convergence of the harmonic extension to the values at the boundary.

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Michelangelo Cavina. 2023-12-13. On a quasi-additivity formula for the capacity on Ahlfors-regular spaces. https://arxiv.org/abs/2312.08297

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