Olives contain oleuropin and hydroxytyrosol. The former is a known anti-inflammatory - you might find this article on oleuropin interesting: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5392257/

There's ongoing work on any benefits of hydroxytyrosol. Chemically, it's an antioxidant, but I don't see any clinical studies...

Also, olives contain oleic acid, which is more effective at activating sirtuins than resveratrol. IMO, that's the key to the Mediterranean Diet's effect on longevity.