Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 3-19
University of Warsaw, Institute of Mathematics
Banacha 2, 02-097 Warszawa, Poland; m.miskiewicz 'at' mimuw.edu.pl
Abstract. The paper proves that a bound on the averaged Jones' square function of a measure implies an upper bound on the measure. Various types of assumptions on the measure are considered. The theorem is a generalization of a result due to Naber and Valtorta in connection with measure bounds on the singular set of harmonic maps.
2010 Mathematics Subject Classification: Primary 28A75, 28A78.
Key words: Reifenberg parametrization, Jones' square number.
Reference to this article: M. Miskiewicz: Discrete Reifenberg-type theorem. Ann. Acad. Sci. Fenn. Math. 43 (2018), 3-19.
https://doi.org/10.5186/aasfm.2018.4301
Copyright © 2018 by Academia Scientiarum Fennica