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arXiv · 1707.00357

Generalized Hölder continuity and oscillation functions

Imre Péter Tóth
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Abstract

We study a notion of generalized Hölder continuity for functions on $\mathbb{R}^d$. We show that for any bounded function $f$ of bounded support and any $r>0$, the $r$-oscillation of $f$ defined as $osc_r f (x):= \sup_{B_r(x)} f - \inf_{B_r(x)} f$ is automatically generalized Hölder continuous, and we give an estimate for the appropriate (semi)norm. This is motivated by applications in the theory of dynamical systems.

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Imre Péter Tóth. 2018-10-11. Generalized Hölder continuity and oscillation functions. https://arxiv.org/abs/1707.00357

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