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arXiv:1504.02585 [math.FA]AbstractReferencesReviewsResources

Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces

Toni Heikkinen, Heli Tuominen

Published 2015-04-10Version 1

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.

Categories: math.FA
Subjects: 46E35, 43A85
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