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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Carleson measures for Bergman spaces and their dual Berezin transforms


Authors: Boo Rim Choe, Hyungwoon Koo and Michael Stessin
Journal: Proc. Amer. Math. Soc. 137 (2009), 4143-4155
MSC (2000): Primary 32A36; Secondary 32A18, 32A37
Published electronically: July 13, 2009
MathSciNet review: 2538575
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Abstract: We introduce the notion of weighted dual Berezin transforms and characterize Carleson measures for weighted Bergman spaces over the ball by a certain BMO property of their dual Berezin transforms.


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Additional Information

Boo Rim Choe
Affiliation: Department of Mathematics, Korea University, Seoul 136-713, Korea
Email: cbr@korea.ac.kr

Hyungwoon Koo
Affiliation: Department of Mathematics, Korea University, Seoul 136-713, Korea
Email: koohw@korea.ac.kr

Michael Stessin
Affiliation: Department of Mathematics, The State University of New York, Albany, New York 12222
Email: stessin@math.albany.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09980-8
PII: S 0002-9939(09)09980-8
Keywords: Carleson measure, Bergman space, dual Berezin transform
Received by editor(s): March 19, 2009
Published electronically: July 13, 2009
Additional Notes: Part of this research was performed during the third author’s visit to Korea University in 2008. He thanks the mathematics department of Korea University and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Science and Engineering Foundation Grant funded by the Korean Government (KOSEF R01-2008-000-20206-0).
Communicated by: Franc Forstneric
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.