A median approach to differentiation bases

Toni Heikkinen*, Juha Kinnunen

*Corresponding author for this work

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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.

Original languageEnglish
Pages (from-to)41-66
Number of pages26
JournalRENDICONTI LINCEI: MATEMATICA E APPLICAZIONI
Volume30
Issue number1
DOIs
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Lebesgue differentiation theorem
  • differentiation bases
  • median maximal function
  • SOBOLEV SPACES
  • BESOV
  • EXTENSION
  • OSCILLATION

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