Factorization theory for a class of Toeplitz + Hankel operators

In this paper we study operators of the form $M(\varphi )=T(\varphi )+H(\varphi )$ where $T(\varphi )$ and $H(\varphi )$ are the Toeplitz and Hankel operators acting on $H^p(\text{T})$ with generating function $\varphi \in L^{\text{iy}}(\text{T})$. It turns out that $M(\varphi )$ is invertible if and only if the function $\varphi$ admits a certain kind of generalized factorization.