Generalized Hölder continuity and oscillation functions

• Published in: arXiv.org
• Main Author: Imre Péter Tóth
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.10.2018
• Subjects: Continuity (mathematics)

We study a notion of generalized H\"older 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 H...