WP Multisite (subdirectory) redirect problem

If I try to access another site without putting the “www.” in front of the main domain, it redirects to the root install.

http://www.mysite.com – works
http://www.mysite.com/subdirectory – works
http://mysite.com – redirects to http://www.mysite.com which is fine
http://mysite.com/subdirectory – redirects to http://www.mysite.com

I think the problem has something to do with this line in my wp-config file:
define( ‘DOMAIN_CURRENT_SITE’, ‘www.mysite.com’ );

Should it not include the “www.”? What should I do to fix it?

If I just remove it in the wp-config file, this is what I get:

http://www.mysite.com – works
http://www.mysite.com/subdirectory – works
http://mysite.com – “Error establishing database connection”
http://mysite.com/subdirectory – “Error establishing database connection”