\(m\)-Berezin transform and compact operators

DOI10.4171/RMI/477zbMath1125.47020MaRDI QIDQ877800

Changyong Zhong, Kyesook Nam, DeChao Zheng

Publication date: 3 May 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1169480034

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Linear operators on function spaces (general) (47B38) Bergman spaces of functions in several complex variables (32A36)

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Cites Work

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• BMO in the Bergman metric on bounded symmetric domains
• An invariant volume-mean-value property
• Compact Toeplitz operators via the Berezin transform on bounded symmetric domains
• Pluriharmonic symbols of commuting Toeplitz operators
• Compact operators on Bergman spaces
• Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
• Toeplitz Operators on the Segal-Bargmann Space
• Compact operators via the Berezin transform
• Heat Flow and Berezin-Toeplitz Estimates
• Approximation and then-Berezin transform of operators on the Bergman space
• A Lipschitz estimate for Berezin’s operator calculus
• COVARIANT AND CONTRAVARIANT SYMBOLS OF OPERATORS