A new characterization of the Sobolev space
Volume 159 / 2003
Studia Mathematica 159 (2003), 263-275
MSC: Primary 46E35.
DOI: 10.4064/sm159-2-7
Abstract
The purpose of this paper is to provide a new characterization of the Sobolev space $W^{1,1}( \mathbb R^n)$. We also show a new proof of the characterization of the Sobolev space $W^{1,p}( \mathbb R^n)$, $1\leq p<\infty $, in terms of Poincaré inequalities.
