Title of article :
Non-stretch mappings for a sharp estimate of the Beurling–Ahlfors operator
Author/Authors :
Chen، نويسنده , , Xingdi and Qian، نويسنده , , Tao، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2014
Abstract :
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 Bañuelos–Wang conjecture and the Iwaniec 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 Bañuelos–Wang conjecture and the Iwaniec conjecture are true.
Keywords :
Beurling–Ahlfors operator , Cauchy operator , Harmonic mapping , Beltrami equation , Principal solution
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications