Cauchy-Schwarz-type inequalities on K\"{a}hler manifolds-II

We establish in this note some Cauchy-Schwarz-type inequalities on compact Kähler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higherdimensional cases. Our proof is to make full use of the mixed Hodge-Riemann bilinear relations due to Dinh and Nguyên. A proportionality problem related to our main result is also proposed.