GENERALIZED COMPOSITION OPERATORS FROM GENERALIZED WEIGHTED BERGMAN SPACES TO BLOCH TYPE SPACES

Abstract

Let H(B) denote the space of all holomorphic functions on the unit ball B of <TEX>$\mathbb{C}^n$</TEX>. Let <TEX>$\varphi$</TEX> = (<TEX>${\varphi}_1,{\ldots}{\varphi}_n$</TEX>) be a holomorphic self-map of B and <TEX>$g{\in}2$</TEX>(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operator <TEX>$C_{\varphi}^gf(z)=\int_{0}^{1}{\mathfrak{R}}f(\varphi(tz))g(tz){\frac{dt}{t}}$</TEX> from generalized weighted Bergman spaces into Bloch type spaces.