  Some Besov-type spaces $B^{s,\tau}_{p,q}(\mathbb{R}^n)$ can be characterized
in terms of the behavior of the Fourier--Haar coefficients. In this article,
the authors discuss some necessary restrictions for the parameters $s$, $\tau$,
$p$, $q$ and $n$ of this characterization. Therefore, the authors measure the
regularity of the characteristic function $\mathcal X$ of the unit cube in
$\mathbb{R}^n$ via the Besov-type spaces $B^{s,\tau}_{p,q}(\mathbb{R}^n)$.
Furthermore, the authors study necessary and sufficient conditions such that
the operation $\langle f, \mathcal{X} \rangle$ generates a continuous linear
functional on $B^{s,\tau}_{p,q}(\mathbb{R}^n)$.
