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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.06433 |
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| _version_ | 1866915012752179200 |
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| author | Chen, Huiling Ye, Shanli |
| author_facet | Chen, Huiling Ye, Shanli |
| contents | Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n,k})_{n,k\geq 0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_{n}=\int_{[0,1)}t^ndμ(t)$, induces, formally, the Derivative-Hilbert operator $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty μ_{n,k}a_k\right)(n+1)z^n , ~z\in \mathbb{D},$$ where $f(z)=\sum_{n=0}^\infty a_nz^n$ is an analytic function in $\mathbb{D}$. We characterize the measures $μ$ for which $\mathcal{DH}_μ$ is a bounded operator on $BMOA$ space. We also study the analogous problem from the $α$-Bloch space $\mathcal{B}_α(α>0)$ into the $BMOA$ space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Derivative-Hilbert operator acting on BMOA space Chen, Huiling Ye, Shanli Functional Analysis Complex Variables Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n,k})_{n,k\geq 0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_{n}=\int_{[0,1)}t^ndμ(t)$, induces, formally, the Derivative-Hilbert operator $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty μ_{n,k}a_k\right)(n+1)z^n , ~z\in \mathbb{D},$$ where $f(z)=\sum_{n=0}^\infty a_nz^n$ is an analytic function in $\mathbb{D}$. We characterize the measures $μ$ for which $\mathcal{DH}_μ$ is a bounded operator on $BMOA$ space. We also study the analogous problem from the $α$-Bloch space $\mathcal{B}_α(α>0)$ into the $BMOA$ space. |
| title | A Derivative-Hilbert operator acting on BMOA space |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2411.06433 |