no, you can't. you can play on PS3 the PS1 games available on PSN that are formatted for PS3/PSP.
Some PSP games are also available or ported to PS3 (or viceversa), like: Everyday Shooter, Super Stardust, Go! Puzzle, Go! Sudoku, Lemmings, Lego Batman, Need for Speed Undercover, Need for Speed Carbon, Gripshift, Full Auto 2: Battlelines, Harry Potter, etc.