Some properties of Sobolev spaces

摘要

The aim of this paper is to present some new characterizations of the Sobolev spaces W~(κ,p)(Ω) where 1 < p < ∞, κ ≥ 2 and Ω is a bounded smooth domain of R~N. For p = 1, we prove same results by replacing W~(κ,1)(Ω) by the BV~κ(Ω) space. As an application we show how to recognize polynomial functions among locally integrable functions.