A proof of Carleson's 𝜀2-conjecture
Jaye, B., Tolsa, X., & Villa, M. (2021). A proof of Carleson's 𝜀2-conjecture. Annals of Mathematics, 194(1), 97-161. https://doi.org/10.4007/annals.2021.194.1.2
Published in
Annals of MathematicsDate
2021Copyright
© 2021 Department of Mathematics, Princeton University.
In this paper we provide a proof of the Carleson 𝜀2-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 𝜀2-square function.
Publisher
Mathematics Department, Princeton UniversityISSN Search the Publication Forum
0003-486XPublication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/99293227
Metadata
Show full item recordCollections
Additional information about funding
B. J. was partially supported by NSF through DMS-1800015 (now DMS-2103534) and the CAREER Award DMS-1847301 (now DMS-2049477). X.T. was partially supported by MTM-2016-77635-P (MICINN, Spain) and 2017-SGR-395 (AGAUR, Catalonia). M.V. was supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh. ...License
Related items
Showing items with similar title or keywords.
-
Uniform rectifiability and ε-approximability of harmonic functions in Lp
Hofmann, Steve; Tapiola, Olli (Centre Mersenne; l'Institut Fourier,, 2020)Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that ... -
ε-approximability of harmonic functions in Lp implies uniform rectifiability
Bortz, Simon; Tapiola, Olli (American Mathematical Society, 2019) -
Uniform rectifiability implies Varopoulos extensions
Hofmann, Steve; Tapiola, Olli (Elsevier, 2021)We construct extensions of Varopolous type for functions f∈BMO(E), for any uniformly rectifiable set E of codimension one. More precisely, let Ω⊂Rn+1 be an open set satisfying the corkscrew condition, with an n-dimensional ... -
Weakly porous sets and Muckenhoupt Ap distance functions
Anderson, Theresa C.; Lehrbäck, Juha; Mudarra, Carlos; Vähäkangas, Antti V. (Elsevier, 2024)We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight w(x)=dist(x,E)−α belongs to the Muckenhoupt class A1, for some α>0, if and only if E⊂Rn is weakly ... -
Rectifiability of RCD(K,N) spaces via δ-splitting maps
Bruè, Elia; Pasqualetto, Enrico; Semola, Daniele (Finnish Mathematical Society, 2021)In this note we give simplified proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via -splitting maps. The arguments are inspired by the Cheeger-Colding ...