Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

Ziwei Li, Dachun Yang and Wen Yuan
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Ziwei Li: Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Dachun Yang: Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Wen Yuan: Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Mathematics, 2021, vol. 9, issue 21, 1-46

Abstract: In this article, the authors study the Lebesgue point of functions from Haj?asz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to these spaces. In case these functions are not locally integrable, the authors also consider their generalized Lebesgue points defined via the ? -medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets.

Keywords: Haj?asz–Sobolev space; Haj?asz–Besov space; Haj?asz–Triebel–Lizorkin space; generalized smoothness; Lebesgue point; capacity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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