What would be the special character for this mathematical notation?
\[DoubleVerticalBar]
behaves like a binary operator (often used to indicate parallel lines in geometry). You probably want
Subsuperscript[\[LeftDoubleBracketingBar] h/3 \[RightDoubleBracketingBar], 0, H] //
TraditionalForm
which gives
Bob Hanlon's comment is closer to what I was expecting, but it may be that m_goldberg's notation may be more correct. In doubt, I'll post this:
(V == HoldForm[A/H^2] Subsuperscript[Abs[HoldForm[h^3/3]], 0, H])