  We prove a Weitzenb\"ock 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 $W^{1,2}$ elliptic estimate
relies on the Aronszajn-Necas-Smith coercive estimate. For generalized strongly
pseudoconvex domains, we improve the Morrey estimate to a weighted $W^{1,2}$
square function estimate, using a generalized Cauchy-Pompieu reproducing
formula and the T1 theorem for singular integrals. We use Van Schaftingen's
notion of cocanceling to study the generalized Levi forms appearing.
