Bounded distance generating function

Question

There is a distance-generating function $\omega(x) : X \rightarrow R $ in the definition of Bregman distance, which is then defined as $V(x,y) = \omega(y) − \omega(x) − \langle\omega^\prime(x), y − x\rangle$. One possible example of $\omega(x)$ is $\frac12\|x\|_2^2$. But is there an example of $\omega(x)$ bounded on the whole space $\mathbb{R}^n$ (bounded both below and above)?