Generalized integral type Hilbert operator acting on weighted Bloch space

Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $${\mathcal{I}}_{{\mu }_{\alpha +1}}(f)(z)={\int }_0^1\frac{f(t)}{(1-tz{)}^{\alpha +1}}d\mu (t)(\alpha >-1)\mathrm{.}$$ The operator ${\mathcal{I}}_{{\mu }_1}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of ${\mathcal{I}}_{{\mu }_{\alpha +1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of ${\mathcal{I}}_{{\mu }_{\alpha +1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.