Submitted Paper

Inserted: 4 nov 2021
Last Updated: 4 nov 2021

Year: 2021

Abstract:

We obtain a new characterization of the higher Sobolev space $W^{m,p}(\mathbb R^n)$, $m\in \mathbb N$ and $p\in (1, +\infty)$ and of the space $BV^m$, the space of functions of higher order bounded variation. The characterizations are in term of BMO-type seminorms. The results unify and substantially extend previous results by Fusco-Moscariello-Sbordone and Farroni-Guarino Lo Bianco-Schiattarella.

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