The easiest way would be to configure web server on customersdomain.com to act as a reverse proxy. In this case it would proxy requests to yourownserver.com or wherever you need.
Another way is to install CSP Gateway on a customersdomain.com. After that connect CSP Gateway to your Cache/Ensemble/InterSystems IRIS instance on yourownserver.com. And connect web server on customersdomain.com to CSP Gateway on customersdomain.com.
Advantage of this approach is that static would be served directly from customersdomain.com server.