Problems sending internally between users

Problems sending internally between users

I have my account set up correctly (as far as I know), the MX records are correct. I can send and receive emails from external accounts, so for example, if I have mydomain.com I can send emails 

from me@gmail.com to me@mydomain.com
from me@mydomain.com to me@gmail.com

but I can't send any emails internally:

from me@mydomain.com to you@mydomain.com

They are in the 'sent' part of the 'me' account, but never turn up in the 'you' part.