Can't remove faucet handles

[MPrice]

Don't know the manufacturer, I just remember it was not one of the big names. the handle is the top 1" or so, down to the bottom of that first ring that you can see.
The cap screws off but then I'm stumped. There is no screw inside or outside. It looks like they should lift off but they are both on there very securely. I've tried WD40 and tapping lightly with a hammer to try to lift them but they do not budge. Any ideas?

 

[Smooky]

You need a handle puller:

http://www.pascospecialty.com/spotlight.php?pid=2&issue=35

http://www.homedepot.com/p/Faucet-Handle-Compression-Sleeve-Puller-HDX168/204218643


https://www.greydock.com/hb-1104a.h...O7rypmJt9QCFZWCswodT_wIhw#product-description

 

[Sponsor]

 

[hj]

TRyunscrewing the "dome" under the handle.