The local Dirichlet integral and applications

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Omar El-Fallah, Karim Kellay, H. Mahzouli
DOI: 10.48550/arxiv.2601.04987
Cited by: 0

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.

Fields of Study & Subjects

Holomorphic and Operator Theory Spectral Theory in Mathematical Physics Advanced Harmonic Analysis Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
8 January 2026
Language
EN
Document type
Preprint