  In this paper we find a pathwise decomposition of a certain class of Brownian
semistationary processes ($\mathcal{BSS}$) in terms of fractional Brownian
motions. To do this, we specialize in the case when the kernel of the
$\mathcal{BSS}$ is given by
$\varphi_{\alpha}\left(x\right)=L\left(x\right)x^{\alpha}$ with
$\alpha\in(-1/2,0)\cup(0,1/2)$ and $L$ a continuous function slowly varying at
zero. We use this decomposition to study some path properties and derive
It\^o's formula for this subclass of $\mathcal{BSS}$ processes.
