I believe UV does not affect digital sensors like it does film so no need for UV filters with digital bodies.
Why add another layer of glass with perhaps lessor optical quality in front of lenses we fret over for price and optical performance?
No UV or clear filters here on any lenses including the 500mm PF and 200-500mm.
For front lens element damage control a lens hood is likely a better option. BCG's Steve P tested filters (search for it) for protective use and found them basically unneeded unless shooting in dusty / sandy environment. Many lenses like the 500 PF are already weather resistant.