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

Author

Listed:
  • 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)

Abstract

In this article, the authors study the Lebesgue point of functions from Hajłasz–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 γ -medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets.

Suggested Citation

  • Ziwei Li & Dachun Yang & Wen Yuan, 2021. "Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness," Mathematics, MDPI, vol. 9(21), pages 1-46, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2724-:d:666103
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    Cited by:

    1. Xianjie Yan & Ziyi He & Dachun Yang & Wen Yuan, 2023. "Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 3056-3116, July.

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