Oscillation of Functions in the Hölder class

2019/05/13 by Mozolyako, Pavel, Nicolau, Artur
#26A16 #42A61 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04911

Abstract

We study the size of the set of points where the α-divided difference of a function in the Hölder class Λ_α is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated in the language of dyadic martingales. Our main technical result in this setting is a sharp estimate of the Hausdorff measure of the set of points where a dyadic martingale with bounded increments has maximal growth.

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