A Bloch type space associated with λ-analytic functions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908914540347392 |
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| author | Wei, Haihua Qian, Kanghui Li, Zhongkai Niu, Yeli |
| author_facet | Wei, Haihua Qian, Kanghui Li, Zhongkai Niu, Yeli |
| contents | For $λ\ge0$, the so-called $λ$-analytic functions are defined in terms of the (complex) Dunkl operators $D_{z}$ and $D_{\bar{z}}$. In the paper we introduce a Bloch type space on the disk ${\mathbb D}$ associated with $λ$-analytic functions, called the $λ$-Bloch space and denoted by ${\mathfrak{B}}_λ({\mathbb D})$. Various properties of the $λ$-Bloch space ${\mathfrak{B}}_λ({\mathbb D})$ are proved. We give a characterization of functions in ${\mathfrak{B}}_λ({\mathbb D})$ by means of the higher-order operators $(D_z\circ z)^n$ for $n\ge2$. A general integral operator is proved to be bounded from $L^{\infty}({\mathbb D})$ onto ${\mathfrak{B}}_λ({\mathbb D})$, and as an application, the dual relation of ${\mathfrak{B}}_λ({\mathbb D})$ and the $λ$-Bergman space ($p=1$) is verified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bloch type space associated with λ-analytic functions Wei, Haihua Qian, Kanghui Li, Zhongkai Niu, Yeli Complex Variables Classical Analysis and ODEs 30H20, 30H10 (Primary), 30G30, 42A45 (Secondary) For $λ\ge0$, the so-called $λ$-analytic functions are defined in terms of the (complex) Dunkl operators $D_{z}$ and $D_{\bar{z}}$. In the paper we introduce a Bloch type space on the disk ${\mathbb D}$ associated with $λ$-analytic functions, called the $λ$-Bloch space and denoted by ${\mathfrak{B}}_λ({\mathbb D})$. Various properties of the $λ$-Bloch space ${\mathfrak{B}}_λ({\mathbb D})$ are proved. We give a characterization of functions in ${\mathfrak{B}}_λ({\mathbb D})$ by means of the higher-order operators $(D_z\circ z)^n$ for $n\ge2$. A general integral operator is proved to be bounded from $L^{\infty}({\mathbb D})$ onto ${\mathfrak{B}}_λ({\mathbb D})$, and as an application, the dual relation of ${\mathfrak{B}}_λ({\mathbb D})$ and the $λ$-Bergman space ($p=1$) is verified. |
| title | A Bloch type space associated with λ-analytic functions |
| topic | Complex Variables Classical Analysis and ODEs 30H20, 30H10 (Primary), 30G30, 42A45 (Secondary) |
| url | https://arxiv.org/abs/2603.25012 |