Weighted $α$-subharmonic measure
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909049655656448 |
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| author | Kuldoshev, Kobiljon Salaeva, Dilnur |
| author_facet | Kuldoshev, Kobiljon Salaeva, Dilnur |
| contents | In this paper, we introduce and study the weighted $α$-subharmonic measure associated with a weight function $ψ$, extending the usual $α$-subharmonic measure and reducing to it when $ψ\equiv -1$.
Furthermore, we study the relationship between the weighted $α$-subharmonic measure and $α$-regular compact sets. We also obtain a characterization of $(α,ψ)$-regularity in terms of the continuity of the corresponding weighted $α$-subharmonic measure. Finally, we prove that if the weighted $α$-subharmonic measure of the compact set $K$ is Hölder continuous with respect to $K$, then it is Hölder continuous everywhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted $α$-subharmonic measure Kuldoshev, Kobiljon Salaeva, Dilnur Complex Variables 32U05, 32U15, 31C45, 35J15 In this paper, we introduce and study the weighted $α$-subharmonic measure associated with a weight function $ψ$, extending the usual $α$-subharmonic measure and reducing to it when $ψ\equiv -1$. Furthermore, we study the relationship between the weighted $α$-subharmonic measure and $α$-regular compact sets. We also obtain a characterization of $(α,ψ)$-regularity in terms of the continuity of the corresponding weighted $α$-subharmonic measure. Finally, we prove that if the weighted $α$-subharmonic measure of the compact set $K$ is Hölder continuous with respect to $K$, then it is Hölder continuous everywhere. |
| title | Weighted $α$-subharmonic measure |
| topic | Complex Variables 32U05, 32U15, 31C45, 35J15 |
| url | https://arxiv.org/abs/2605.16851 |