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arXiv · 1805.11967

Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space

Songxiao Li·Jizhen Zhou
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Abstract

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_\mu=(\mu_{n+k})_{n,k\geq 0}$ with entries $\mu_{n,k}=\mu_{n+k}$ induces the operator $$ \mathcal{H}_\mu(f)(z)=\sum^\infty_{n=0}\left(\sum^\infty_{k=0}\mu_{n,k}a_k\right)z^n $$ on the space of all analytic functions $f(z)=\sum^\infty_{n=0}a_nz^n$ in the unit disk $\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\mathcal{H}_\mu$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\mathcal{H}_\mu$ from $\alpha$ Bloch type spaces to Bloch space and BMOA.

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Songxiao Li, Jizhen Zhou. 2018-05-30. Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space. https://arxiv.org/abs/1805.11967

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