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

Abstract

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix ${\mathcal{H}}_{\mu }=({\mu }_{n+k}{)}_{n,k\ge 0}$ with entries ${\mu }_{n,k}={\mu }_{n+k}$ induces the operator $${\mathcal{H}}_{\mu }(f)(z)=\sum _{n=0}^{\infty }\left(\sum _{k=0}^{\infty }{\mu }_{n,k}{a}_k\right)z^n$$ on the space of all analytic functions $f(z)={\sum }_{n=0}^{\infty }{a}_n{z}^n$ 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.

References in corpus (1)

• Hankel matrices acting on the Hardy space $H^1$ and on Dirichlet spaces