We study vector measure. Integration and spaces of p- integrable functions with respect to a vector measure are considered .We establish the spaces of integrable and vector functions with respect to vector measures of convex range and factorization of operators from - spaces. We show some integral identities and inequalities for entire functions and their applications to the coherent state transform, with positive multilinear operators acting on weighted - spaces. We construct the structures of the modulation spaces and multilinear pseudo-differential operators. We show the localization...