This question is mainly for understanding the history behind homogeneous spaces.
There is extensive literature on Besov and Triebel-Lizorkin spaces. For instance, see the standard textbook:
https://link.springer.com/book/10.1007/978-3-642-16830-7
One thing that I never really understood is why do we use homogeneous spaces instead of non-homogeneous ones ?.
Is there some original motivation as to why these spaces were used ?
