Haven't flown in a while need help
 

Hi, I booked a flight to the UK thru American Airlines and its operated by British Aiways for the outward bound flight and most of the homeward bound flight except for the last connecting flight at JFK to Ohare which is operated by AA.
My question is, will my luggage be transfered from the BA operated flight to the AA operated flight at JFK or do I have to collect my luggage and check in with AA at JFK? This was purchased as a round trip at the same time. Thanks for the help.