## Hankel operators on the Bergman space of bounded symmetric domains

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- by Ke He Zhu PDF
- Trans. Amer. Math. Soc.
**324**(1991), 707-730 Request permission

## Abstract:

Let $\Omega$ be a bounded symmetric domain in ${\mathbb {C}^n}$ with normalized volume measure $dV$. Let $P$ be the orthogonal projection from ${L^2}(\Omega ,dV)$ onto the Bergman space $L_a^2(\Omega )$ of holomorphic functions in ${L^2}(\Omega ,dV)$. Let $\overline P$ be the orthogonal projection from ${L^2}(\Omega ,dV)$ onto the closed subspace of antiholomorphic functions in ${L^2}(\Omega ,dV)$. The "little" Hankel operator ${h_f}$ with symbol $f$ is the operator from $L_a^2(\Omega )$ into ${L^2}(\Omega ,dV)$ defined by ${h_f}g = \overline P (fg)$. We characterize the boundedness, compactness, and membership in the Schatten classes of the Hankel operators ${h_f}$ in terms of a certain integral transform of the symbol $f$. These characterizations are further studied in the special cases of the open unit ball and the poly-disc in ${\mathbb {C}^n}$.## References

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## Additional Information

- © Copyright 1991 American Mathematical Society
- 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