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


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.


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