Chord-arc curves and the Beurling transform

• 成果类型: Article
• 署名作者: Astala, K.; Gonzalez, M. J.
• 署名单位: University of Helsinki; Universidad de Cadiz
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0630-8
• 发表日期: 2016
• 页码: 57-81
• 关键词: mappings; SPACES

摘要

We study the relation between the geometric properties of a quasicircle and the complex dilatation of a quasiconformal mapping that maps the real line onto . Denoting by S the Beurling transform, we characterize Bishop-Jones quasicircles in terms of the boundedness of the operator on a particular weighted space, and chord-arc curves in terms of its invertibility. As an application we recover the boundedness of the Cauchy integral on chord-arc curves.