Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Chen, Xingdi^1,2  Qian, Tao² 

[1] Huaqiao Univ, Dept Math, Quanzhou 362021, Fujian, Peoples R China

[2] Univ Macau, Fac Sci & Technol, Dept Math, Macau, Peoples R China

关键词: Beurling-Ahlfors operator;    Cauchy operator;    Harmonic mapping;    Beltrami equation;    Principal solution;   

DOI  :  10.1016/j.jmaa.2013.11.010

来源: Elsevier

【 摘 要 】

In this paper we identify certain classes of non-stretch mappings that enjoy a sharp estimate of the Beurling-Ahlfors operator. We first make use of a property of subharmonic functions to prove that the Banuelos-Wang conjecture and the lwaniec conjecture are true for a class of mappings that satisfy a quasilinear conjugate Beltrami equation. By utilizing the principal solutions of Beltrami equations, we further explicitly construct some classes of non-stretch mappings for which the Bailuelos-Wang conjecture and the lwaniec conjecture are true. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free