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

Published online by Cambridge University Press:  23 July 2004

JIE XIAO
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's, NL A1C 5S7, Canadajxiao@math.mun.ca
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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.

Keywords

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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Footnotes

This work was supported in part by the NSERC of Canada.