It is very important to properly attach pergola posts when installing a pergola over a deck.  Pergolas are not very heavy because there aren't any roof or snow loads.  The main concern is how the structure will react under high wind conditions.  Most deck builders bolt pergola support posts to the frame of the deck using (2) 1/2"x6" lag screws with washers per post.  This technique is the same as attaching a rail post.  Pergolas are top heavy and can sway in the wind without lateral bracing and can act experience strong uplift forces as the pergola acts as a sail.  Attaching sections of rail in between pergola posts will strengthen the pergola.  Installing 45 degree bracing in between the post and header beam will also increase stability.  Using 6x6's for support posts will further strengthen the structure.  Deck Lok brackets are an option for extremely windy areas and hurricane zones.