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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

BMO on strongly pseudoconvex domains: Hankel operators, duality and $ \overline\partial$-estimates


Authors: Huiping Li and Daniel H. Luecking
Journal: Trans. Amer. Math. Soc. 346 (1994), 661-691
MSC: Primary 47B35; Secondary 32A37, 32F20, 32H10, 46E15
MathSciNet review: 1273537
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Abstract: We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to $ BMO$ plus analytic. (Here we mean the Bergman metric $ BMO$ of Berger, Coburn and Zhu.) In the course of the proof we obtain new $ \overline \partial $-estimates that may be of independent interest. Some applications include a decomposition of $ BMO$ similar to the classical $ {L^\infty } + \widetilde{{L^\infty }}$, and two characterizations of the dual of $ VMO$ (which is also a predual of $ BMO$).

In addition, we obtain some partial results on the boundedness of Hankel operators in $ {L^1}$ norm.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1273537-5
PII: S 0002-9947(1994)1273537-5
Keywords: Hankel operator, $ BMO$, strongly pseudoconvex domain
Article copyright: © Copyright 1994 American Mathematical Society