Notation for $y$-restriction?

Question

$f(x) \; \{a<x<b\}$ can be written $[f(x)]^b_a$. Is there an equivalent notation for $f(x) \; \{a<y<b\}$?

Edited to add: for instance,

Answer 1

As far as I know there isn't, but you could probably make it clear with $[f(x)]_{y \geq a}^{y \leq b}$