RIEMANN–STIELTJES OPERATORS ON WEIGHTED BLOCH AND BERGMAN SPACES OF THE UNIT BALL

Abstract

Riemann–Stieltjes integrals are considered as linear operators on weighted Bloch and Bergman spaces of the open unit ball in several complex variables. For weighted Bloch spaces, boundedness, compactness and weak compactness of Riemann–Stieltjes operators are characterized by means of certain growth properties of holomorphic symbols. For weighted Bergman spaces, some criteria are given for Riemann–Stieltjes operators with holomorphic symbols to be bounded, compact and of Schatten–von Neumann's ideal.