A refinement of the Schwarz-Pick estimates and the Carathéodory metric in several complex variables

DOI10.1007/S10473-024-0409-3MaRDI QIDQ6499114

Tai Shun Liu, Xiaosong Liu

Publication date: 8 May 2024

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Other generalizations of function theory of one complex variable (32A30)

Cites Work

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• The generalized Schwarz-Pick estimates of arbitrary order on the unit polydisk
• Schwarz-Pick estimates for partial derivatives of arbitary order of bounded holomorphic functions in the unit ball of \(\mathbb C^n\)
• The Schwarz-Pick lemma of high order in several variables
• The high order Schwarz-Pick lemma on complex Hilbert balls
• Higher-order Schwarz-Pick estimates for holomorphic self-mappings on classical domains
• Some refined Schwarz-Pick lemmas
• Schwarz-Pick inequalities for derivatives of arbitrary order
• Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of \(\mathbb C^n\)
• Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions
• On Generalized Schwarz‐Pick Estimates
• A Schwarz–Pick lemma for the norms of holomorphic mappings in Banach spaces
• Generalized Schwarz-Pick estimates
• Refined Bohr's theorem for holomorphic mappings in several complex variables
• Note on Schwarz-Pick estimates for bounded and positive real part analytic functions

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