Pointwise inequalities and approximation in fractional Sobolev spaces
Volume 149 / 2002
Studia Mathematica 149 (2002), 147-174
MSC: 46E35, 31B15, 41A25, 41A63.
DOI: 10.4064/sm149-2-5
Abstract
We prove that a function belonging to a fractional Sobolev space $L^{\alpha ,p}({\mathbb R}^n)$ may be approximated in capacity and norm by smooth functions belonging to $C^{m,\lambda } ({\mathbb R}^n)$, $0 < m + \lambda < \alpha $. Our results generalize and extend those of [12], [4], [14], and [11].
