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Riemann–Stieltjes Operators on Weighted Bloch and Bergman Spaces of the Unit Ball
Author(s) -
Xiao Jie
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005484
Subject(s) - riemann–stieltjes integral , mathematics , holomorphic function , bergman space , unit sphere , compact space , pure mathematics , several complex variables , conformal map , bounded function , mathematical analysis , bergman kernel , integral equation
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.