Scaled oscillation and level sets

Scaled oscillation and level sets
HTML articles powered by AMS MathViewer

by Iqra Altaf, Marianna Csörnyei and Bobby Wilson PDF

Proc. Amer. Math. Soc. 150 (2022), 2913-2924 Request permission

We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.

References

Giovanni Alberti, Generalized N-property and Sard theorem for Sobolev maps, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 23 (2012), no. 4, 477–491. MR 2999558, DOI 10.4171/RLM/641
Giovanni Alberti, Stefano Bianchini, and Gianluca Crippa, Structure of level sets and Sard-type properties of Lipschitz maps, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12 (2013), no. 4, 863–902. MR 3184572
Giovanni Alberti, Stefano Bianchini, and Gianluca Crippa, A uniqueness result for the continuity equation in two dimensions, J. Eur. Math. Soc. (JEMS) 16 (2014), no. 2, 201–234. MR 3161282, DOI 10.4171/JEMS/431
Zoltán M. Balogh and Marianna Csörnyei, Scaled-oscillation and regularity, Proc. Amer. Math. Soc. 134 (2006), no. 9, 2667–2675. MR 2213746, DOI 10.1090/S0002-9939-06-08290-6
Marianna Csörnyei and Bobby Wilson, Tangents of $\sigma$-finite curves and scaled oscillation, Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 1, 1–12. MR 3505664, DOI 10.1017/S030500411500081X
Loukas Grafakos, Classical Fourier analysis, 2nd ed., Graduate Texts in Mathematics, vol. 249, Springer, New York, 2008. MR 2445437
Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. MR 1333890, DOI 10.1017/CBO9780511623813