Let $H(\theta, \boldsymbol{Z}, \lambda)$ is defined on $\Theta \times D \times(0, \pi)$, where $\Theta$ is a compact subset of $\mathbf{R}$ and $D$ is an open subset of $\mathbf{R}$. $H(\theta, \cdot , \cdot)$ is continuous with respect to $\theta$. What are the conditions to state that the exists a function $h$ such that
$$sup _\theta | H(\theta, \boldsymbol{Z}, \lambda) | \leq h(\boldsymbol{Z}, \lambda) ?$$
If so, is it possible to have more information about the properties of $h$?