Document Type : Research Paper

Authors

• Ayyoub Manavi ¹
• Mostafa Hassanlou ²

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

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

Abstract

Let ${\mathcal{H}}_{\mu }=({\mu }_{n+k}{)}_{n,k\ge 0}$ with entries ${\mu }_{n,k}={\mu }_{n+k}$ induces the operator ${\mathcal{H}}_{\mu }(f)(z)=\sum _{n=0}^{\mathrm{\infty }}\left(\sum _{k=0}^{\mathrm{\infty }}{\mu }_{n,k}{a}_k\right)z^n$ on the space of all analytic functions $f(z)=\sum _{n=0}^{\mathrm{\infty }}{a}_n{z}^n$ 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.

Keywords

• Boundedness
• Compactness
• Hilbert matrix operator
• Operator
• Zygmund space