If you reached this article you are probably trying to host a Google hangout. The first thing you did was probably email some of your friends. If some of your friends tell you they never received the email, you are not crazy, it’s because their email system is not working correctly right now.
See this post from Dori, a Google Community Manager back on July 17th.
This is a known issue that the team is investigating and looking to fix. In the meantime, to ensure that your participants receive the link to join your HOA, please open your HOA, then grab the URL from the top of the browser and either share it with your participants in a limited Google+ post or send it to them via email.
And as of August 22nd, the emails are still not being sent correctly. It seems to only affect certain accounts.
Please post back if you have any further updates on this or if you are also having the same issues.