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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hankel operators on the Bergman space of the unit polydisc


Author: Huiping Li
Journal: Proc. Amer. Math. Soc. 120 (1994), 1113-1121
MSC: Primary 47B35; Secondary 32A37, 47B07, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1994-1176483-6
MathSciNet review: 1176483
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Abstract: Let $ D$ be the unit polydisc in $ {\mathbb{C}^n}$. Let $ {H^2}(D)$ be the Bergman space of $ D$. In this paper, by using the integral representations of solutions to the $ \overline \partial $-equations, we give function theoretic characterizations of functions $ f \in {L^2}(D)$ such that the Hankel operators $ {H_f}$ from the Bergman space to $ {L^2}(D)$ are bounded and compact, respectively.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1176483-6
Article copyright: © Copyright 1994 American Mathematical Society