On harmonic quasiregular mappings in Bergman spaces

2025/07/25 by Suman Das, Das, Suman, Antti Rasila +1
Mathematics · #30C62 #30H20 #31A05 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2507.19158

openalex publication_date 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical result of Hardy and Littlewood says that if f=u+iv is analytic in the unit disk \mathbbD and u is in the harmonic Bergman space a^p (00 such that every univalent harmonic function f (and the partial derivatives f_θ, rf_r) is of class a^p. This result extends nicely to harmonic quasiconformal mappings in \mathbbD.

Citations

• Note on real and imaginary parts of harmonic quasiregular mappings
• On the coefficients estimate of K-quasiconformal harmonic mappings
• Zygmund theorem for harmonic quasiregular mappings
• Zygmund's theorem for harmonic quasiregular mappings
• On a problem of Pavlović involving harmonic quasiconformal mappings
• Riesz type theorems for κ-pluriharmonic mappings, invariant harmonic quasiregular mappings and harmonic quasiregular mappings
• Riesz and Kolmogorov inequality for harmonic quasiregular mappings
• Hp spaces of several variables

Related

• Zygmund's theorem for harmonic quasiregular mappings
• Note on real and imaginary parts of harmonic quasiregular mappings
• Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem
• Lipschitz spaces and harmonic mappings
• Uniformly locally univalent harmonic mappings