[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2016.24.1.15

ESSENTIAL NORM OF THE PULL BACK OPERATOR

Shuan, Tang (School of Mathematics Sciences Soochow University)
Chong, Wu (School of Mathematics Southwest Jiaotong University)

Publication Information

Korean Journal of Mathematics / v.24, no.1, 2016 , pp. 15-25 More about this Journal

Abstract

We obtain some estimations of the essential norm of a pull back operator induced by quasi-symmetric homeomorphisms. As a corollary, we deduce the compactness criterion of this operator.

Keywords

Pull-pack operator; Quasi-conformal map; Boundary dilatation; Essential norm;

Citations & Related Records

Reference

1	A. Beurling and L. V. Ahlfors, The boundary correspondence under quasi-conformal mappings, Acta Mathematica. 96 (1956), 125-142. DOI
2	G. Cui, Integrably asymptotic affine homeomorphisms of the circle and Teichmuller spaces, Sci. China Ser. A 43 (2000), 267-279. DOI
3	A. Douady and C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), 23-48. DOI
4	F. P. Gardiner and D. Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992), 683-736. DOI
5	Y. Hu and Y. Shen, On quasisymmetric homeomorphisms, Israel J. Math. 191 (2012), 209-226. DOI
6	C. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.
7	J. H. Shapiro, The essential norm of a composition operator. Ann of Math. 125 (1987), 375-404 DOI
8	Y. Shen, Weil-peterssen Teichmuller space, arXiv:1304.3197v1 [math.CV] 11 Apr. 2013.
9	Y. Shen and H. Wei, Universal Teichmuller space and BMO, Adv. Math. 234 (2013), 129-148. DOI