Journal of the
Korean Mathematical Society JKMS

Let $H(B)$ denote the space of all holomorphic functions on the unit ball $B$ of $\mathbb C^n$. Let $\varphi=(\varphi_1,\ldots,\varphi_n)$ be a holomorphic self-map of $B$ and $g \in H(B)$ with $g(0)=0$. In this paper we study the boundedness and compactness of the generalized composition operator $$ C_\varphi^g f(z)= \int_0^1 \Re f(\varphi(tz)) g(tz)\frac{dt}{t} $$ from generalized weighted Bergman spaces into Bloch type spaces.

Keywords: generalized composition operator, generalized weighted Bergman space, Bloch type space

MSC numbers: Primary 47B35, Secondary 30H05