On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1

• 成果类型: Article
• 署名作者: Nazarov, Fedor; Tolsa, Xavier; Volberg, Alexander
• 署名单位: University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; ICREA; Autonomous University of Barcelona; Michigan State University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0120-7
• 发表日期: 2014
• 页码: 237-321
• 关键词: principal values

摘要

We prove that if mu is a d-dimensional Ahlfors-David regular measure in , then the boundedness of the d-dimensional Riesz transform in L (2)(mu) implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of mu.