Inserted: 23 jan 2020
Last Updated: 19 apr 2021
Journal: Journal of Mathematical Analysis and Applications
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.