Approximation by H\"older functions in Besov and Triebel-Lizorkin spaces
Functional Analysis
2015-04-13 v1
Abstract
In this paper, we show that Besov and Triebel-Lizorkin functions can be approximated by a H\"older continuous function both in the Lusin sense and in norm. The results are proven in metric measure spaces for Haj{\l}asz-Besov and Haj{\l}asz-Triebel-Lizorkin functions defined by a pointwise inequality. We also prove new inequalities for medians, including a Poincar\'e type inequality, which we use in the proof of the main result.
Keywords
Cite
@article{arxiv.1504.02585,
title = {Approximation by H\"older functions in Besov and Triebel-Lizorkin spaces},
author = {Toni Heikkinen and Heli Tuominen},
journal= {arXiv preprint arXiv:1504.02585},
year = {2015}
}