A median approach to differentiation bases
Research output: Contribution to journal › Article › Scientific › peer-review
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.
|Number of pages||26|
|Journal||RENDICONTI LINCEI: MATEMATICA E APPLICAZIONI|
|Publication status||Published - 2019|
|MoE publication type||A1 Journal article-refereed|
- Lebesgue differentiation theorem, differentiation bases, median maximal function, SOBOLEV SPACES, BESOV, EXTENSION, OSCILLATION