Wiener-Hopf factorization for a class of oscillatory symbols

Two classes of 2 x 2 matrix symbols involving oscillatory functions are con sidered, one of which consists of triangular matrices. An equivalence theor em is obtained, concerning the solution of Riemann-Hilbert problems associa ted with each of them. Conditions for existence of canonical generalized fa ctorization are established, as well as boundedness conditions for the fact ors. Explicit formulas are derived for the factors, showing in particular t hat only one of the columns needs to be calculated. The results are applied to solving a corona problem.