On the first page of an old paper of Bogovskii, the notation $W_p^l(\Omega)$ and $L_p^l(\Omega)$ is used without explanation.

I assume that $W_p^l(\Omega)$ denotes the usual Sobolev space of functions in $L_p(\Omega) := \{ f : \Omega \to \mathbb{R} : f \textrm{ is measurable and } \int_{\Omega} |f|^p < \infty \}$ whose weak derivatives of order up to $l$ are also in $L_p(\Omega)$.

I have not seen the notation $L_p^l(\Omega)$ used before, but according to the first sentence of this paper it is a "Sobolev space". What does this notation mean?