Let $f$ and $g$ be real functions. I quite like the notations $f \ll g$ to mean $f \in O(g)$ and $f \sim g$ to mean $\lim \frac fg = 1$. For example it is nice to be able to write out chains of asymptotic inequalities like "$f \ll g \ll h$" rather than $f \in O(g) \subset O(h)$. The latter also doesn't have a natural analogue if I wanted to instead express "$f \in o(g)$ and $g \in o(h)$".
Are there similar notations which are commonly understood to mean $f \in o(g)$ or $f \in \Theta(g)$? For instance $f \lll g$ seems like a natural candidate for the former but I haven't seen anyone use it to mean that.