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 Iμα+1(f)(z)=∫01f(t)(1−tz)α+1dμ(t)(α>−1).$$ {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). $$The operator Iμ1$$ {\mathcal{I}}_{\mu_1} $$ has been extensively studied recently. The aim of this paper is to study the boundedness (resp. compactness) of Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ 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 Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ acting between Bloch type spaces, and between logarithmic Bloch spaces. [ABSTRACT FROM AUTHOR]