The $\mathrm{\partial }\bar{\mathrm{\partial }}$-problem for a differential forms with boundary value in currents sense defined in a contractible completely strictly pseudoconvex domain of a complex manifold

We solve the $\mathrm{\partial }\bar{\mathrm{\partial }}$-problem for the differential forms of class $C^{\mathrm{\infty }}$ with boundary value in currents sense defined on a contractible completely strictly pseudoconvex domain of a complex manifold.