Generalized integral type Hilbert operator acting between weighted Bloch spaces

Let μ $$ \mu be a finite Borel measure on [ 0,1 ) \left[0,1\right) . In this paper, we consider the generalized integral type Hilbert operator I α + 1 ( f z = ∫ 0 t − d > {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). The {\mathcal{I}}_{\mu_1} has been extensively studied recently. aim of paper is to study boundedness (resp. compactness) acting from normal weight Bloch space into another same kind. As consequences our study, get completely results for between spaces, and logarithmic spaces.