Abstract
Let µ be a finite Borel measure on [0 ,1). In this
paper, we consider the generalized integral type Hilbert operator I µ α
+ 1 ( f ) ( z ) = ∫ 0 1 f ( t ) ( 1 − tz ) α + 1 d µ ( t ) ( α
> − 1 ) . The operator I µ 1 has been extensively studied
recently. The aim of this paper is to study the boundedness(resp.
compactness) of I µ α + 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 I µ α + 1 acting between Bloch
type spaces, logarithmic Bloch spaces among others.