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Mapping properties of weighted Bergman projection operators on Reinhardt domains


Authors: Željko Čučković and Yunus E. Zeytuncu
Journal: Proc. Amer. Math. Soc. 144 (2016), 3479-3491
MSC (2010): Primary 32A25; Secondary 32A26, 32A36
Published electronically: February 1, 2016
MathSciNet review: 3503715
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Abstract: We show that on smooth complete Reinhardt domains, weighted Bergman projection operators corresponding to exponentially decaying weights are unbounded on $ L^p$ spaces for all $ p\not =2$. On the other hand, we also show that the exponentially weighted projection operators are bounded on Sobolev spaces on the unit ball.


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Additional Information

Željko Čučković
Affiliation: Department of Mathematics and Statistics, University of Toledo, Toledo, Ohio 43606
Email: zeljko.cuckovic@utoledo.edu

Yunus E. Zeytuncu
Affiliation: Department of Mathematics and Statistics, University of Michigan, Dearborn, Dearborn, Michigan 48128
Email: zeytuncu@umich.edu

DOI: https://doi.org/10.1090/proc/12984
Keywords: Bergman projection, exponential weights, $L^p$ regularity, Sobolev regularity
Received by editor(s): September 3, 2015
Received by editor(s) in revised form: September 21, 2015, and October 11, 2015
Published electronically: February 1, 2016
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society