We prove a Weitzenböck identity for general pairs of constant-coefficient homogeneous first-order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural 1/2 boundary conditions. Our proof of the (Formula presented.) elliptic estimate relies on the Aronszajn–Ne (Formula presented.) as–Smith coercive estimate. For generalized strongly pseudoconvex domains, we improve the Morrey estimate to a weighted (Formula presented.) square function estimate, using a generalized Cauchy–Pompeiu reproducing formula and the (Formula presented.) theorem for singular integrals. We use Van Schaftingen's notion of cocanceling to study the generalized Levi forms appearing.