Abstract
In this paper, we show that Besov and Triebel-Lizorkin functions can be approximated by a Hölder continuous function both in the Lusin sense and in norm. The results are proven in metric measure spaces for Hajłasz-Besov and Hajłasz-Triebel-Lizorkin functions defined by a pointwise inequality. We also prove new inequalities for medians, including a Poincaré type inequality, which we use in the proof of the main result.
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