A median approach to differentiation bases

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Authors

Date

2019

Department

Department of Mathematics and Systems Analysis

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Mcode

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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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DOI

10.4171/RLM/835

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

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https://urn.fi/URN:NBN:fi:aalto-201905062746

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[article-cris] Perustieteiden korkeakoulu / SCI