Just Upgraded to Mojave and started getting the Out of Application Memory box I have just migrated to Mojave and with no applications open, except whatever runs in the background, I receive the Out of Application Memory panel.  The only app it shows as running is Finder.  I am running on a Mac Mini with 815 Gbytes available on my system drive. I did not have this error before upgrading to Mojave.
You are NOT out of memory ! 

That notification is false.

It shows you are using 3.1GB out of 8GB, so you have 5GB free Memory.

So your hardware is fine. 

That must be a bug in Mojave, not sure which one. For some reason the Applications are reporting wrong Memory usage, even so the Activity monitor does not show that.

You also have a lot 3D party apps running. Some might not be Mojave compatible, so for now Just turn them all off, Presto Scan...and others.

It is also advised to completely remove MacKeeper, since it has been reported as Malware, and Mac OS X is perfectly safe without it.

Possible fix:

Go to Dropbox icon > Cog wheel at the bottom left > Preferences Disable "Enable Finder Integration"