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arXiv · 2601.04987

The local Dirichlet integral and applications

Omar El-Fallah·Karim Kellay·Houssame Mahzouli
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Abstract

We study the local Dirichlet integral of distance functions and their behavior within the harmonic Dirichlet space. We provide estimates for the local Dirichlet integral of distance functions, which allow us to study their membership in the algebra of multipliers of the Dirichlet space. We give sufficient condition for a closed subset of the unit circle to be polar and we also examine cyclicity in the harmonic Dirichlet spaces.

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Omar El-Fallah, Karim Kellay, Houssame Mahzouli. 2026-01-08. The local Dirichlet integral and applications. https://arxiv.org/abs/2601.04987

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