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arXiv · 1504.02585

Approximation by H\"older functions in Besov and Triebel-Lizorkin spaces

Toni Heikkinen·Heli Tuominen
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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.

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Toni Heikkinen, Heli Tuominen. 2015-04-10. Approximation by H\"older functions in Besov and Triebel-Lizorkin spaces. https://arxiv.org/abs/1504.02585

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