In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study composition operators between them in detail. particular, characterize bounded compact spaces.

The boundedness and the compactness of generalized weighted composition operators from weighted Bergman spaces into Zygmund-type spaces are investigated in this paper. Moreover, we give some estimates for the essential norm of these operators.

An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...

The boundedness and compactness of weighted composition operators from Dirichlet type spaces to weighted type spaces on the unit ball of Cn are characterized in this paper. Mathematics subject classification (2010): Primary 47B38; Secondary 46E15.