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

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The $$\partial \bar {\partial }$$ -Problem for the Differential Forms with Boundary Value in Currents Sense Defined in a Contractible Completely Strictly Pseudoconvex Domain of a Complex Manifold