First steps in Dovecot; IMAP not working

[Moi]

> I always install "locate" and whenever I change anything do as root
"/usr/bin/updatedb"
> then you can type
> "locate *.log"

Thank you. It worked and I now have several log files to check.

In the meantime, I've tried once again to send a message to "mailtest" from
an outside address; this time, I got an error reply:

This report relates to a message you sent with the following header fields:

  Message-id: <00e201d2290f$67da8c70$378fa550$@mac.com>
  Date: Tue, 18 Oct 2016 09:15:21 +0200
  From: Moi
  To: 'Mail Test' <mailtest at barbu.sytes.net>
  Subject: Test

Your message cannot be delivered to the following recipients:

  Recipient address: mailtest at barbu.sytes.net
  Reason: Illegal host/domain name found
<end of reply>

Yet another area with a problem; at least this is now a valid reason for it
to not work.
Is this a misconfiguration of my DNS server?