Some prevalent results about strongly monoHolder functions

被引：12
|
作者：
Clausel, Marianne [2 ]
Nicolay, Samuel [1 ]
机构：
[1] Univ Liege, Inst Math, B-4000 Liege, Sart Tilman, Belgium
[2] Univ Paris Est, CNRS, Lab Analyse & Math Appliquees, UMR 8050, F-94010 Creteil, France
来源：
NONLINEARITY | 2010年 / 23卷 / 09期
关键词：
HAUSDORFF DIMENSION; GRAPHS;
D O I：
10.1088/0951-7715/23/9/004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the typical behaviour of strongly monoHolder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHolder functions. We then use the notion of prevalence to show that the functions of C-alpha(R-d) are almost surely strongly monoHolder with Holder exponent a. Finally, we prove that for any alpha is an element of (0, 1) on a prevalent set of C-alpha(R-d) the Hausdorff dimension of the graph is equal to d + 1 - alpha.
引用
收藏
页码：2101 / 2116
页数：16
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