A class of compound vector-valued problem and factorization of matrix function

In this article, we consider a class of compound vector-valued problem on upper-half plane ℂ+, which consists of vector Riemann problem along a closed contour in ℂ+ with matrix coefficient in Hölder class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.