W1p trace theorem on a half-space
= W1p trace theorem on a half-space
{title2=$T:W^{1,p}(\mathbb R_+^n)\to L^p(\mathbb R^{n-1})$}
For $1\leq p<\infty$, boundary restriction on smooth functions extends uniquely to a bounded linear map $T:W^{1,p}(\mathbb R_+^n)\to L^p(\mathbb R^{n-1})$. The estimate follows by applying the <fundamental theorem of calculus> on normal line segments and then integrating over the boundary variables.