I'm not sure what the scare quotes are about but if you point out what I'm misrepresenting I can try to explain it a little better.
Compression acts on the amplitude of the entire audio signal, not "quiet frequencies". You can start here: https://en.wikipedia.org/wiki/Dynamic_range_compression
Normalization as it normally is used is offline process where you up the gain of the whole audio so that the loudest noise is 0dB.
I'm not sure what the scare quotes are about but if you point out what I'm misrepresenting I can try to explain it a little better.