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

Abstract

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.