The two best things to reduce sound transmission are to add mass to the floor assembly (be sure floor can hold additional weight though), and uncouple the drywall ceiling on the floor below from the floor joists. This is done with resilient channels attached to the underside of the floor joists, then the drywall attaches to a rubber membrane in the channel. Adding a layer of homasote under flooring may help add some mass and absorb sound.

floor assembly illustration

This may also sound obvious, but recessed can lights allow a lot of sound to be transmitted from floor to floor. So you may want to consider other lighting options if you want to reduce sound transmission.

A layer of UNFACED fiberglass insulation in the joist space will also help absorb sound.