So 1500 years is a bit of a stretch. This is when the Crusaders occupied Jerusalem. The Arabs and Europeans were all occupiers. The earliest owners of the site, that still exist, are the Jews. It is clearly Jewish property. If you want to see Muslim Arab property go to Mecca. I'm sure it's nice this time of year.
Passport control employees at Ben Gurion airport to strike between 11 A.M. and 1 P.M. (Haaretz)
from the article: Likud lawmaker: Jews should be allowed freer access to Temple Mount