Sobolev extension in a simple case - Drake Marjorie; Fefferman Charles; Ren Kevin; Skorobogatova Anna (Advanced Nonlinear Studies)
In this paper, we establish the existence of a bounded, linear extension operator T:L2,p(E)→L2,p(R2) $T :L^{2,p}\left(E\right)→ L^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R2 ${\mathbb{R}}^{2}$ contained in a line.