If you're using ESP to provide Frontend Authentication for your Exchange environment, it's possible that your Office 365 clients are unable to see calendar information for your On Premise Exchange Users.
Add two "Autodiscover" directories to your "Pre-Authorization Excluded Directories"
(Only Necessary if you Do Not have "Delegate to Server" set as your "Client Authentiaction Mode").
Navigate to your Exchange Virtual Service > Autodiscover Sub Virtual Service > ESP Options > "Pre-Authorization Excluded Directories. Add the below directories space separated.