The easiest solution, and less expensive in the short run, would be fillers to contour the lower eyelid and fill in the depressions. The best product for this area is Restylane, followed by Belotero. If you want a permanent fix, then a lower eyelid fat transposition blepharoplasty is your best option, to reposition fat from a "hill" into a "hollow". Choose an experienced oculoplastics surgeon.
There are a variety of options for the sunken hollow under eyes. 1) filler injection, done in office, which lasts around 2 years. 2) fat injection, done under local anesthesia, which last many years but not as predictable. 3) tear trough implant which are permanent and effective but more invasive procedure. Another option might be lower blepharoplasty with fat repositioning where the fat/bags are repositioned to fill in the hollow sunken area. Best to see an oculoplastic specialist for evaluation.