A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II
We continue the study of the space $BV^\alpha(\mathbb R^n)$ of functions with bounded fractional variation in $\mathbb R^n$ and of the distributional fractional Sobolev space $S^{\alpha,p}(\mathbb R^n)$, with $p\in [1,+\infty]$ and $\alpha\in(0,1)$, considered in the previous works arXiv:1809.08575 and arXiv:1910.13419. We first define the space $BV^0(\mathbb R^n)$ and establish the …