A Schwarz lemma for the modulus of a vector-valued analytic function

DOI10.1090/S0002-9939-2010-10578-6zbMath1217.30022OpenAlexW2068336396WikidataQ124808405 ScholiaQ124808405MaRDI QIDQ3085060

Miroslav Pavlović

Publication date: 28 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10578-6

zbMATH Keywords

Schwarz lemmaLipschitz conditionvector-valued analytic functions

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (18)

Schwarz lemma for pluriharmonic functions ⋮ A Schwarz lemma for harmonic functions in the real unit ball ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Some characterizations of slice regular Lipschitz type spaces ⋮ On holomorphic functions on negatively curved manifolds ⋮ A Schwarz–Pick lemma for the norms of holomorphic mappings in Banach spaces ⋮ SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL ⋮ The Schwarz-Pick lemma and Julia lemma for real planar harmonic mappings ⋮ Lipschitz constants for the real part and modulus of analytic mappings on a negatively curved surface ⋮ On harmonic functions and the Schwarz lemma ⋮ On harmonic functions on surfaces with positive Gauss curvature and the Schwarz lemma ⋮ Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions ⋮ COEFFICIENT ESTIMATES, LANDAU’S THEOREM AND LIPSCHITZ-TYPE SPACES ON PLANAR HARMONIC MAPPINGS ⋮ Another look at the Landau theorem ⋮ Generalized versions of Lipschitz conditions on the modulus of holomorphic functions ⋮ LIPSCHITZ SPACES AND BOUNDED MEAN OSCILLATION OF HARMONIC MAPPINGS ⋮ A Schwarz–Pick lemma for the modulus of holomorphic mappings ⋮ A Harnack inequality on the boundary of the unit ball

Cites Work

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• Addendum to ``Strong Hardy-Littlewood theorems for analytic functions and mappings of finite distortion. [Math. Z. 249, No. 3, 597--611 (2005; Zbl 1067.30042)]
• Equivalent norms on Lipschitz-type spaces of holomorphic functions
• On K. M. Dyakonov's paper: ``Equivalent norms on Lipschitz-type spaces of holomorphic functions
• Strong Hardy-Littlewood theorems for analytic functions and mappings of finite distortion
• Holomorphic functions and quasiconformal mappings with smooth moduli

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