  In this paper, we consider the Dirichlet problem for a new class of augmented
Hessian equations. Under sharp assumptions that the matrix function in the
augmented Hessian is regular and there exists a smooth subsolution, we
establish global second order derivative estimates for the solutions to the
Dirichlet problem in bounded domains. The results extend the corresponding
results in the previous paper [11] from the Monge-Ampere type equations to the
more general Hessian type equations.
