A median approach to differentiation bases

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openAccess

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Journal Title

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2019

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Mcode

Degree programme

Language

en

Pages

26
41-66

Series

RENDICONTI LINCEI: MATEMATICA E APPLICAZIONI, Volume 30, issue 1

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.

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Keywords

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

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Citation

Heikkinen, T & Kinnunen, J 2019, ' A median approach to differentiation bases ', RENDICONTI LINCEI: MATEMATICA E APPLICAZIONI, vol. 30, no. 1, pp. 41-66 . https://doi.org/10.4171/RLM/835