In reading about $L_p$ spaces and $\ell_p$ norms and metrics, I have seen a wide variety of different notations for the same thing.
Is there a standard convention for when to use lowercase $\ell$ vs uppercase $L$, as well as when to use a subscript vs a superscript $p$?
I have seen $L_p$ space, $L^p$ space, $\ell_p^k$ space, $L_p$ metric, $\ell^p$ metric, $\ell^p$ norm, and almost every combination of lowercase, uppercase, subscript, and superscripts possible, in various books and papers.
So far it seems almost random to me and subject to the author's whims, but perhaps there is some guiding principle that most people use here that I'm not seeing.