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). ...

Let φ be a holomorphic self-map of the open unit polydisk U in C and p, q > 0. In this paper, the generally weighted Bloch spaces B log(U ) are introduced, and the boundedness and compactness of composition operator Cφ from B p log(U ) to B log(U ) are investigated.

In this paper, we give a new characterization for the boundedness and compactness of differences of generalized weighted composition operators from the Bloch space into weightedtype spaces. Moreover, we give some estimates for the essential norm of these operators. Mathematics subject classification (2010): 30D45, 47B38.

In this paper, some classes of concerned multiplication operators consisting analytic and hyperbolic functions are defined considered. Furthermore, properties such as boundedness compactness the new discussed. Finally, a general class weighted Bloch is characterized by metric spaces.