  The solvability of the Riemann-Hilbert boundary value problem on the real
line is described in the case when its matrix coefficient admits a Wiener-Hopf
type factorization with bounded outer factors but rather general diagonal
elements of its middle factor. This covers, in particular, the almost periodic
setting. Connections with the corona problem are discussed. Based on those,
constructive factorization criteria are derived for several types of triangular
2-by-2 matrices.
