  In this note, we obtain sharp bounds for the Green's function of the
linearized Monge-Amp\`ere operators associated to convex functions with either
Hessian determinant bounded away from zero and infinity or Monge-Amp\`ere
measure satisfying a doubling condition. Our result is an affine invariant
version of the classical result of Littman-Stampacchia-Weinberger for uniformly
elliptic operators in divergence form. We also obtain the $L^{p}$ integrability
for the gradient of the Green's function in two dimensions. As an application,
we obtain a removable singularity result for the linearized Monge-Amp\`ere
equation.
