This might interest you: https://mathoverflow.net/questions/28147/why-do-we-care-about-lp-spaces-besides-p-1-p-2-and-p-infty
– John11Dec 06 '18 at 08:41
for applications of functional analysis, there is already a popular question: https://math.stackexchange.com/questions/1556307/what-are-the-applications-of-functional-analysis
– supinfDec 06 '18 at 08:43