Sobolev extension in a simple case

Abstract

In this paper, we establish the existence of a bounded, linear extension operator T:L2,p(E)→L2,p(R2) $T :{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R2 ${\mathbb{R}}^{2}$ contained in a line.

Keywords

• sobolev extension
• linear extension
• whitney extension
• calderón–zygmund decomposition
• 46e35