Can You Put a Psone Game from the Playstation Store on to the Psp?

lets say i buy Metal gear solid off the playstation store from the ps3. can i transfer it to the psp?
and also do u need to buy it seperate or does the download work with both systems?

Suggestion:

all ps1 classics are ps3 and psp compatible
just register the psp to your ps3 account that downloaded it and copy to the psp ( triangle/copy )
you can download on up to 5 ps3 or psp systems that are linked to the account .