JFK Airport Terminal 4 to 3?

I will be arriving at JFK Airport Terminal 4 by Emirates Airlines. Then I need to go to Terminal 3 to catch a Delta Airlines flight to Rochester. I will be having two big luggage bags with me. Can I check-in those luggage bags at Terminal 4 in the Delta Airlines Counter ? Or can I request the Delta Airlines authorities to transfer those luggages for me to terminal 3 ?