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Journal of the London Mathematical Society 2004 70(1):199-214; doi:10.1112/S0024610704005484
© 2004 by London Mathematical Society
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© The London Mathematical Society

Riemann–Stieltjes Operators on Weighted Bloch and Bergman Spaces of the Unit Ball

Jie Xiao

Department of Mathematics and Statistics, Memorial University of Newfoundland St John's, NL A1C 5S7, Canada, jxiao{at}math.mun.ca

Received 18 June 2003. Revision received 7 January 2004.

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.


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