I may consider them as L^2 then following theorem holds.
https://en.wikipedia.org/wiki/Plancherel_theorem
https://de.wikipedia.org/wiki/Satz_von_Plancherel
https://de.wikipedia.org/wiki/Parsevalsche_Gleichung
https://ms.mcmaster.ca/craig/craig-pde-chap5.pdf
Also keen to learn if there is any other theorems.