Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds

We establish an a priori $C^2$-estimate for complex Hessian equations on compact Hermitian manifolds. As an application, we obtain a regularity result for solutions to complex Hessian equation with densities of the right hand side depending on the solution. This generalizes Székelyhidi–Tosatti’s result to the setting of complex Hessian equations on Hermitian manifolds.