A representation theorem for standard weighted harmonic mappings with an integer exponent and its applications

DOI10.1016/j.jmaa.2016.07.035zbMath1345.31017OpenAlexW2499327099MaRDI QIDQ739520

David Kalaj, Xingdi Chen

Publication date: 18 August 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.07.035

zbMATH Keywords

Radó-Kneser-Choquet theorem\(\bar\alpha\)-harmonic mappingsweighted Laplacian operator

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (8)

Lipschitz continuity for weighted harmonic functions in the unit disc ⋮ A series expansion for generalized harmonic functions ⋮ Lipschitz continuity for solutions of the \(\bar{\alpha}\)-Poisson equation ⋮ On a weighted harmonic Green function and a theorem of Littlewood ⋮ A representation theorem for standard weighted harmonic mappings with an integer exponent and its applications ⋮ Some geometric properties of complex-valued kernel \(\alpha \)-harmonic mappings ⋮ Schwarz lemma for solutions of the \(\alpha\)-harmonic equation ⋮ Some coefficient estimates on real kernel 𝛼-harmonic mappings

Cites Work

• Unnamed Item
• Unnamed Item
• A priori estimate of gradient of a solution of a certain differential inequality and quasiconformal mappings
• Differential operators for a scale of Poisson type kernels in the unit disc
• Some properties of a class of elliptic partial differential operators
• \((K, K^{\prime})\)-quasiconformal harmonic mappings
• A representation theorem for standard weighted harmonic mappings with an integer exponent and its applications
• Poisson integrals for standard weighted Laplacians in the unit disc
• A partial differential equation arising in conformal mapping
• (K,K')-Quasiconformal harmonic mappings of the upper half plane onto itself
• QUASICONFORMAL SOLUTIONS OF POISSON EQUATIONS
• Generalized Schwarz-Pick estimates
• Landau-Type Theorems for Solutions of a Quasilinear Differential Equation

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