Almost Lipschitz-continuous wavelets in metric spaces via a new randomization of dyadic cubes

作者：Hytoenen Tuomas; Tapiola Olli^*

来源：Journal of Approximation Theory, 2014, 185: 12-30.

DOI：10.1016/j.jat.2014.05.017

• Metric space
• Dyadic cube
• Doubling property
• Wavelets
• Spline functions

In any quasi-metric space of homogeneous type, Auscher and Hytonen recently gave a construction of orthonormal wavelets with Holder-continuity exponent eta > 0. However, even in a metric space, their exponent is in general quite small. In this paper, we show that the Holder-exponent can be taken arbitrarily close to 1 in a metric space. We do so by revisiting and improving the underlying construction of random dyadic cubes, which also has other applications.

• 出版日期2014-9