Multipliers for logarithmic Cauchy integrals in the ball

Abstract

Let B n denote the unit ball in $$ \mathbb{C} $$ n , n ≥ 1. Let $$ \mathcal{K} $$ 0(n) denote the class of functions defined for z ∈ B n as a constant plus the integral of the kernel log(1/(1 −〈z, ζ〉)) against a complex Borel measure on the sphere {ζ ∈ $$ \mathbb{C} $$ n ,: |ζ| = 1}. Properties of holomorphic functions g such that fg ∈ $$ \mathcal{K} $$ 0(n) for all f ∈ $$ \mathcal{K} $$ 0(n) are studied. The extended Cesaro operators are investigated on the spaces $$ \mathcal{K} $$ 0(n), n ≥ 1. Bibliography: 15 titles.