What can be done for hollowness under cheek bones?

Fillers can be used to give back lost volume. I suggest seeking the advice of a filler expert who uses cannulas to reshape the face with very little complications.  Best, Dr. Emer.

Hollowness under the cheek bones could possibly be improved with injectable fillers or surgically placed implants.  Pictures of you or an exam would be needed to determine if you might be a good candidate for either of these treatments.  

 When patients have hollowness under the cheek bones, cheek implants  can augment the projection of the maxilla. Cheek implants are manufactured in a variety of sizes and shapes( malar and sub-malar), are composed of Silastic, and are inserted through an intra-oral approach under a brief general anesthetic as an outpatient surgical procedure.

This a good question but unfortunately photos of your face are required to see and comment on any hollow areas of your face.  If the cheeks are the ideal aesthetic shape and there are hollows below, dermal fillers seem the most appropriate (I prefer Perlane).  If the cheeks are in need of augmentation and there are hollows, Cheek Augmentation with Cheek Implants should be considered.  Hope this helps.