A median approach to differentiation bases

  • Toni Heikkinen

    Aalto University, Finland
  • Juha Kinnunen

    Aalto University, Finland
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Abstract

We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann–Feller differentiation bases. Our main result gives several characterizations for the differentiation property in terms of the corresponding median maximal function. As an application, we study pointwise behaviour in Besov and Triebel–Lizorkin spaces, where functions are not necessarily locally integrable. Most of our results apply also for functions defined on metric measure spaces.

Cite this article

Toni Heikkinen, Juha Kinnunen, A median approach to differentiation bases. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 1, pp. 41–66

DOI 10.4171/RLM/835