Solution
= Solution
The <Sobolev fundamental theorem of calculus on lines> gives, for almost every $x$,
$$
\Delta_i^hu(x)=\int_0^1D_i u(x+the_i)\,dt.
$$
Apply the <Minkowski integral inequality> and translation invariance of <Lebesgue measure>:
$$
\lVert\Delta_i^hu\rVert_{L^2(V)}
\leq\int_0^1\lVert D_i u(\,cdot+the_i)\rVert_{L^2(V)}dt
\leq\lVert D_i u\rVert_{L^2(U)}.
$$
The restriction on $h$ ensures that every translated copy used above lies in $U$.