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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 ${\mathbb {C}^n}$.
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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