Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mathcal{ H}_{ \mu,\alpha}=(\mu_{ n,k,\alpha})_{ n,k\geq 0}$ with entries $\mu_{ n,k,\alpha}=\int_{ [0,1)}\frac{ \Gamma(n+\alpha)}{ n!\Gamma(\alpha)}t^{ n+k}d\mu(t)$ formally induces the operator $$\mathcal{ H}_{ \mu,\alpha}(f)(z)=\sum_{ n=0}^{ \infty}\left(\sum_{ k=0}^{ \infty} \mu_{ n, k,\alpha} a_{ k}\right)z^{ n} $$ on the space of all analytic functions $f(z)=\sum_{ k=0}^{ \infty}a_{ k}z^{ k}$ in the unit disc $\mathbb{ D}$. In this paper, we characterize the measures $\mu$ for which $\mathcal{ H}_{ \mu,\alpha}$ ($\alpha\geq 2$) is a bounded (resp., compact) operator from the Bloch type space $\mathscr{ B}_{ \beta}$ ($0<\beta<\infty$) into $\mathscr{ B}_{ \alpha-1}$. We also give a necessary condition for which $\mathcal{ H}_{ \mu,\alpha}$ is a bounded operator by acting on Bloch type spaces for general cases.
Categories: math.CV