Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 53-66

A NOTE ON QUASISYMMETRIC HOMEOMORPHISMS

Shuan Tang and Pengcheng Wu

Guizhou Normal University, School of Mathematics Sciences
Guiyang 550001, P.R. China; tsaflyhigher 'at' 163.com

Guizhou Normal University, School of Mathematics Sciences
Guiyang 550001, P.R. China; wupc 'at' gznu.edu.cn

Abstract. By means of some integral operators and kernel functions, we characterize when a sense preserving homeomorphism h on the unit circle S¹ is quasisymmetric, symmetric or p-integrable asymptotic affine. As an application, we use these results to characterize the pull-back operator, induced by a quasisymmetric homeomorphism on S¹.

2010 Mathematics Subject Classification: Primary 30C62; Secondary 30F60, 32G15.

Key words: Quasisymmetric homeomorphisms, Douady–Earle extension, integral operator, kernel functions, pull-back operator.

Reference to this article: S. Tang and P. Wu: A note on quasisymmetric homeomorphisms. Ann. Acad. Sci. Fenn. Math. 45 (2020), 53-66.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4502