Remarks on the Bourgain–Brezis–Mironescu Approach to Sobolev Spaces
Remarks on the Bourgain–Brezis–Mironescu Approach to Sobolev Spaces
For a function $f\in L_{\rm loc}^p(\mathbb R^n)$ the notion of $p$-mean variation of order 1, $\mathsf{V}^{p}_{1} (f,\mathbb R^n)$ is defined. It generalizes the concept of F. Riesz variation of functions on the real line $\mathbb R^1$ to $\mat