Invertibility properties of matrix Wiener-Hopf plus Hankel integral operators

We consider matrix Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line with Fourier symbols presenting some even properties (which in particular include unitary matrix-valued functions), and also with Fourier symbols which contain sectorial matrices. In both situations, different conditions are founded to ensure the operators invertibility, one-sided invertibility, Fredholm property, and the so-called n and d-normal properties. An example is provided to illustrate the proposed theory.