Characterizing Weighted Composition Operators on Weighted-Type High-Order Growth Spaces via the Component Function $φ_p$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912651553013760 |
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| author | Quang, Thai Thuan |
| author_facet | Quang, Thai Thuan |
| contents | Let $ψ$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $φ$ be a holomorphic self-map of $\BB$, associated with normal weights $ν$ and $μ$. We consider the weighted composition operator $ W_{ψ,φ} : \mathcal H_ν^{(n)} \to \mathcal H_μ^{(m)}, \quad n,m \in \N,$ acting between weighted-type high-order growth spaces. Unlike previous studies that involve the full symbol $φ$, this paper establishes characterizations of the boundedness, compactness, and asymptotic norm estimates of $W_{ψ,φ}$ \emph{solely in terms of the symbol $ψ$ and a single component function $φ_p$ of $φ$}, offering a new approach to the analysis of such operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Weighted Composition Operators on Weighted-Type High-Order Growth Spaces via the Component Function $φ_p$ Quang, Thai Thuan Complex Variables Primary 47B37, Secondary 30H30, 30H40, 47B33, 47B38, 47B91 Let $ψ$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $φ$ be a holomorphic self-map of $\BB$, associated with normal weights $ν$ and $μ$. We consider the weighted composition operator $ W_{ψ,φ} : \mathcal H_ν^{(n)} \to \mathcal H_μ^{(m)}, \quad n,m \in \N,$ acting between weighted-type high-order growth spaces. Unlike previous studies that involve the full symbol $φ$, this paper establishes characterizations of the boundedness, compactness, and asymptotic norm estimates of $W_{ψ,φ}$ \emph{solely in terms of the symbol $ψ$ and a single component function $φ_p$ of $φ$}, offering a new approach to the analysis of such operators. |
| title | Characterizing Weighted Composition Operators on Weighted-Type High-Order Growth Spaces via the Component Function $φ_p$ |
| topic | Complex Variables Primary 47B37, Secondary 30H30, 30H40, 47B33, 47B38, 47B91 |
| url | https://arxiv.org/abs/2510.14187 |