$(m, ψ, δ)-$capacity and its properties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914058203037696 |
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| author | Kuldoshev, Kobiljon |
| author_facet | Kuldoshev, Kobiljon |
| contents | In this paper, we introduce the concept of the generalized $(m, ψ, δ)-$capacity in the complex space $\mathbb{C}^n$, within the class of $m-$subharmonic functions. We give a relation between $(m, ψ, δ)-$capacity and $(m, ψ, δ)-$subharmonic measure. Moreover, we prove that the capacity vanishes on $m-$polar sets and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $(m, ψ, δ)-$capacity and its properties Kuldoshev, Kobiljon Complex Variables 32U05, 32U20 In this paper, we introduce the concept of the generalized $(m, ψ, δ)-$capacity in the complex space $\mathbb{C}^n$, within the class of $m-$subharmonic functions. We give a relation between $(m, ψ, δ)-$capacity and $(m, ψ, δ)-$subharmonic measure. Moreover, we prove that the capacity vanishes on $m-$polar sets and vice versa. |
| title | $(m, ψ, δ)-$capacity and its properties |
| topic | Complex Variables 32U05, 32U20 |
| url | https://arxiv.org/abs/2509.22440 |