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.

中文翻译：

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Hölder类中的函数振荡

我们研究的点的集合，其中的尺寸α在支架类Λ功能的分频的差异_α是通过一个固定的正数为界下方。我们的结果是从它们的离散类似物中获得的，这些类似物可以用二进mar语言来表达。在这种情况下，我们的主要技术成果是对点集的豪斯道夫测度进行了精确估计，在该点集上，有界增量的二叉mar具有最大的增长。