Factorization in the Space of Henstock-Kurzweil Integrable Functions

In this work, we extend the factorization theorem of Rudin and Cohen to $HK(\mathbb{R})$, the space  of Henstock-Kurzweil integrable functions. This implies a factorization for the isometric spaces  $\mathcal{A}_{C}$ and  $\mathcal{B}_{C}$. We also study in this context the Banach algebra of functions $HK(\mathbb{R})\cap BV(\mathbb{R})$, which is also a dense subspace of $L^2(\mathbb{R})$. In some sense this subspace is analogous to $L^1(\mathbb{R})\cap L^2(\mathbb{R})$. However, while $L^1(\mathbb{R}) \cap L^2(\mathbb{R})$  factorizes as $L^1(\mathbb{R})  \cap  L^2(\mathbb{R})  * L^1(\mathbb{R})$,  via the convolution operation *, it is shown in the paper that $HK(\mathbb{R})\cap BV(\mathbb{R}) * L^1(\mathbb{R})$ is a Banach subalgebra of $HK(\mathbb{R})\cap BV(\mathbb{R})$.