A note on quasisymmetric homeomorphisms

Abstract

By means of some integral operators and kernel functions, we characterize when a sense preserving homeomorphism h on the unit circle S 1 is quasisymmetric, symmetric or pintegrable asymptotic affine. As an application, we use these results to characterize the pull-back operator, induced by a quasisymmetric homeomorphism on S 1 . 1 π¨∆ φ h (ζ, z)ψ(z) dx dy, ζ ∈ ∆.