Hankel operators on the Bergman space of bounded symmetric domains

Author:
Ke He Zhu

Journal:
Trans. Amer. Math. Soc. **324** (1991), 707-730

MSC:
Primary 47B35; Secondary 47B10

DOI:
https://doi.org/10.1090/S0002-9947-1991-1093426-6

MathSciNet review:
1093426

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Abstract: Let be a bounded symmetric domain in with normalized volume measure . Let be the orthogonal projection from onto the Bergman space of holomorphic functions in . Let be the orthogonal projection from onto the closed subspace of antiholomorphic functions in . The "little" Hankel operator with symbol is the operator from into defined by . We characterize the boundedness, compactness, and membership in the Schatten classes of the Hankel operators in terms of a certain integral transform of the symbol . These characterizations are further studied in the special cases of the open unit ball and the poly-disc in .

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1093426-6

Article copyright:
© Copyright 1991
American Mathematical Society