Solvability of inhomogeneous Cauchy–Riemann equation in spaces of functions with a system of uniform weight estimates

Abstract

We obtain an analog of the H¨ormander theorem on solvability of the ∂-problem in spaces of functions satisfying a system of uniform estimates. The result is formulated in terms of the weight sequence determining the space. We apply the results for multipliers of projective and inductiveprojective weight spaces of entire functions and for convolution operators in the Roumieu spaces of ultradifferentiable functions.