Generalized Holder Continuity and Oscillation Functions

被引：0

作者：

Toth, Imre Peter ^{[1
,2
]}

机构：

[1] MTA BME Stochast Res Grp, Budapest, Hungary

[2] Budapest Univ Technol & Econ, Dept Stochast, Budapest, Hungary

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2018年 / 21卷 / 04期

关键词：

Holder continuity; Function oscillation; Regularisation; Supremum smoothing; BILLIARD FLOWS;

D O I：

10.1007/s11040-018-9292-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a notion of generalized Holder continuity for functions on Rd. We show that for any bounded function f of bounded support and any r > 0, the r- oscillation of f defined as oscrf (x) := sup Br (x) f - infBr (x) f is automatically generalized Holder continuous, and we give an estimate for the appropriate (semi) norm. This is motivated by applications in the theory of dynamical systems.

引用

页数：18

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