live above (someone or something)
To make one's home above someone or something. I live above a musician, and he's constantly keeping me awake with his practicing. I lived above a convenience store when I was a college student, so I never had to go far to get household essentials.
live above someone or something
and live over someone or somethingto live in a place that is at a higher level than someone or something; to dwell directly over someone or something. We used to live above a small grocery store. Now we live over a student, who often has noisy parties.