The local Dirichlet integral and applications
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918278202392576 |
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| author | El-Fallah, Omar Kellay, Karim Mahzouli, Houssame |
| author_facet | El-Fallah, Omar Kellay, Karim Mahzouli, Houssame |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The local Dirichlet integral and applications El-Fallah, Omar Kellay, Karim Mahzouli, Houssame Classical Analysis and ODEs Complex Variables Functional Analysis 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. |
| title | The local Dirichlet integral and applications |
| topic | Classical Analysis and ODEs Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2601.04987 |