‎In this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes‎. ‎Also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎Moreover‎, ‎compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...

In this paper, we determine the structure of the space of multipliers of the range of a composition operator $C_varphi$ that induces by the conditional expectation between two $L^p(Sigma)$ spaces.

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined an infinite rooted tree. We discuss, through its connection with composition operators, boundedness and compactness operator. addition, discuss norm spectrum, consider when such can be isometry. then apply these results to Lipschitz space weighted Banach spaces, as well H...