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arXiv · 1905.04911

Oscillation of Functions in the H\"older class

Pavel Mozolyako·Artur Nicolau
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Abstract

We study the size of the set of points where the $\alpha$-divided difference of a function in the H\"older class $\Lambda_\alpha$ 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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Pavel Mozolyako, Artur Nicolau. 2019-05-13. Oscillation of Functions in the H\"older class. https://arxiv.org/abs/1905.04911

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