Cauchy and Bergman projection, sharp gradient estimates and certain operator norm equalities

DOI10.1080/17476933.2019.1574771OpenAlexW2923669843MaRDI QIDQ5239195

Petar Melentijević

Publication date: 22 October 2019

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2019.1574771

zbMATH Keywords

gradient estimateBergman projectionBloch spaceoperator normunit ballSiegel upper-half spaceCauchy projection\(\mathcal{M}\)-invariant gradient

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Cites Work

• Cauchy transform and Poisson's equation
• Norm of the Cauchy transform
• On optimal recovery of a holomorphic function in the unit ball of \(\mathbb{C}^ n\)
• Elliptic partial differential equations of second order
• Extremum problems in the theory of analytic functions
• Bloch space and the norm of the Bergman projection
• On the optimal constant for the Bergman projection onto the Bloch space
• Norm of the Bergman Projection
• Bloch Functions in Several Complex Variables, I
• Bloch functions in several complex variables. II.
• Norm of the Bergman projection onto the Bloch space with M-invariant gradient norm
• Spaces of Holomorphic Functions in the Unit Ball
• Projections, the Weighted Bergman Spaces, and the Bloch Space
• The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators
• Norm of the Bergman projection onto the Bloch space

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