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RESEARCH PRODUCT

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

Michele VillaBenjamin JayeXavier Tolsa

subject

Pure mathematicsConjectureMathematics::Classical Analysis and ODEsTangentMetric Geometry (math.MG)Jordan curve theoremsymbols.namesakeMathematics (miscellaneous)Mathematics - Analysis of PDEsMathematics - Metric GeometryMathematics - Classical Analysis and ODEssymbolsClassical Analysis and ODEs (math.CA)FOS: MathematicsStatistics Probability and Uncertainty28A75 42B20MathematicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2019-09-18
https://dx.doi.org/10.48550/arxiv.1909.08581