Published Paper

Inserted: 23 jan 2020
Last Updated: 19 apr 2021

Journal: Journal of Mathematical Analysis and Applications
Year: 2020
Doi: 10.1016/j.jmaa.2020.124298

Abstract:

In the recent literature certain BMO-type seminorms provide characterizations of Sobolev functions. In the same order of ideas, we obtain the norm of the gradient of a function in $L^p(\Omega)$, where $\Omega\subset \mathbb R^n$, $n>1$ and $p>1$, as limit of BMO-type seminorms involving families of pairwise disjoint sets with arbitrary orientation, the sets being not necessarily cubes or tessellation cells. An analogous result is obtained when rotations are not allowed.

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