On solvability of inhomogeneous Cauchy–Riemann equation in functional spaces with a system of uniform estimates

We obtain an analog of the Hörmander theorem on solvability of the $\overline\partial$-problem in spaces of functions satisfying a system of uniform estimates. The result is formulated in terms of the weight sequence which determines the space. We give some applications for multipliers of projective and inductive-projective weight spaces of entire functions and for convolution operators in the Roumieu spaces of ultradifferentiable functions.