A converse to the Schwarz lemma for planar harmonic maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:497

Article

Brevig, Ole Fredrik¹  Ortega-Cerda, Joaquim^2,3  Seip, Kristian⁴ 

[1] Univ Oslo, Dept Math, N-0851 Oslo, Norway

[2] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain

[3] Barcelona Grad Sch Math, Gran Via 585, Barcelona 08007, Spain

[4] Norwegian Univ Sci & Technol NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

关键词: Hardy spaces;    Planar harmonic maps;    Schwarz lemma;   

DOI  :  10.1016/j.jmaa.2020.124908

来源: Elsevier

【 摘 要 】

A sharp version of a recent inequality of Kovalev and Yang on the ratio of the (H-1)* and H-4 norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for the Wirtinger derivatives at the origin for harmonic self-maps of the unit disc which fix the origin. (C) 2020 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free