A proof of Carleson’s $\varepsilon^2$-conjecture

Pages 97-161 from Volume 194 (2021), Issue 1 by Benjamin Jaye, Xavier Tolsa, Michele Villa

Abstract

In this paper we provide a proof of the Carleson $\varepsilon ^2$-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson $\varepsilon ^2$-square function.

Keywords
, , ,
Mathematical Subject Classification

Primary 2000: ,

DOI
https://doi.org/10.4007/annals.2021.194.1.2
MR
4276285
zbMATH
7375201
Milestones
Received: 20 October 2019
Revised: 17 March 2021
Accepted: 16 April 2021
Published online: 23 June 2021

Authors

Benjamin Jaye

School of Mathematics, Georgia Tech, Atlanta, Georgia, 30332, USA

Xavier Tolsa

ICREA, Passeig Lluís Companys 23 08010 Barcelona, Catalonia; Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia; and Centre de Recerca Matemàtica, 08193 Bellaterra, Catalonia

Michele Villa

Department of Mathematics and Statistics, University of Jyväskylä, Finland and Research Unit of Mathematical Sciences, Oulu, Finland