FRACTIONAL CAUCHY TRANSFORMS, MULTIPLIERS AND CESARO OPERATORS

Let B-n denote the unit ball in C-n, n >= 1. Given an alpha > 0, let K-alpha(n) denote the class of functions defined for z is an element of B-n by integrating the kernel (1 - < z, zeta >)(-alpha) against a complex Borel measure on the sphere {zeta is an element of C-n : |zeta| = 1}. We study properties of the holomorphic functions g such that f(g) is an element of K-alpha(n) for all f is an element of K-alpha(n). Also, we investigate extended Cesaro operators on K-alpha(n).