Properties of Besov and Q_p spaces in terms of the Schwarzian derivative of harmonic mappings

2024/08/17 by Hugo Arbeláez, Rodrigo Hernández, Arbeláez, Hugo +3
Mathematics · #30H25 #30H30 #31A05 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2408.09062

openalex publication_date 2024/08/17 · openalex created_date 2024/09/14 · openalex updated_date 2026/07/28

Abstract

In this paper we give a characterization of log J_f belongs to \widetildeB_p or \widetildeQ_p spaces for any locally univalent sense-preserving harmonic mappings f defined in the unit disk, using the Schwarzian derivative of f and Carleson meseaure. In addition, we introduce the classes BT_p and QT_p, based on the Jacobian operator, and begin a study of these.

Related

• Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian DERIVATIVE
• Harmonic pre-Schwarzian and its applications
• On the pre-Schwarzian and Schwarzian derivatives of log-harmonic mappings
• Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm
• Affine and linear invariant families of harmonic mappings