\( \mathrm {L}^p\) Bounds for Square Roots of Elliptic Systems

In the situation of Chap. 14 , we have shown that the operator \(L^{\frac {1}{2}}\) is an isomorphism \(\mathbb {W}^{1,2}_D(O) \to \mathbb {L}^2(O)\) . In this chapter we study when we can replace the integrability parameter \(p=2\) by some other number \(p\in (1,\infty )\) .