Hilbert matrix operator on Zygmund spaces

Document Type : Research Paper


1 Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran

2 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran


Let $\mathcal{H}_\mu=(\mu_{n+k})_{n,k\geq0}$ with entries $\mu_{n,k}=\mu_{n+k}$ induces the operator $\mathcal{H}_\mu(f)(z)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty}\mu_{n,k}a_k\right)z^n$ on the space of all analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in the unit disk $\mathbb{D}$, where $\mu$ is a positive Borel measure on the interval $[0, 1)$. In this paper, we characterize the boundedness and compactness of the operator $\mathcal{H}_\mu$ on Zygmund type spaces.


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Volume 13, Issue 2
July 2022
Pages 1585-1589
  • Receive Date: 20 August 2021
  • Revise Date: 24 September 2021
  • Accept Date: 12 October 2021