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

Li, Huiping; Luecking, Daniel H.

doi:10.1090/S0002-9947-1994-1273537-5

BMO on strongly pseudoconvex domains: Hankel operators, duality and $\overline \partial$-estimates
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by Huiping Li and Daniel H. Luecking PDF

Trans. Amer. Math. Soc. 346 (1994), 661-691 Request permission

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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Hankel operators on the Bergman space of strongly pseudoconvex domains

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