International connecting flight from LAX to Beijing Capital Airport luggage inquire

Not sure if I understood what you're asking with the information you've posted. You mentioned collecting your luggage vs. the airline checking them through, this implies that PEK is not your final destination? If it is not, more information is needed (such as: is your next flight a domestic flight somewhere in China? What airline [to see if they offer check-through baggage service]? etc.) If PEK is your final destination, then you'd just pick up your luggage at baggage claim after clearing immigration.