The local Dirichlet integral and applications
Classical Analysis and ODEs
2026-01-09 v1 Complex Variables
Functional Analysis
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.
Cite
@article{arxiv.2601.04987,
title = {The local Dirichlet integral and applications},
author = {Omar El-Fallah and Karim Kellay and Houssame Mahzouli},
journal= {arXiv preprint arXiv:2601.04987},
year = {2026}
}