Quasisymmetric graphs and Zygmund functions

Leonid V. Kovalev and Jani Onninen

Abstract: A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class Λ*. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.

Journal: Journal d'Analyse Mathematique 118 (2012), no. 1, 343-361.

DOI: 10.1007/s11854-012-0039-x