  Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real
line are studied in view of their invertibility, one sided-invertibility,
Fredholm, and semi-Fredholm properties. This is done in two different cases:
(i) when the Fourier symbols of the operators are unitary functions, and (ii)
when the Fourier symbols are related with sectorial elements appearing in
factorizations of functions originated by the Fourier symbols of the operators.
The obtained result for the case (i) may be viewed as a Douglas-Sarason type
theorem for Wiener-Hopf plus Hankel operators.
