Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces

2015/04/10 by Toni Heikkinen, Heli Tuominen, Heikkinen, Toni +1
Mathematics · #43A85 #46E35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A85 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1504.02585

arxiv created 2015/04/10 · arxiv updated 2015/04/13

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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