Kruse, KarstenKarstenKruse2021-11-152021-11-152022Complex Variables and Elliptic Equations 67: 2676 - 2707 (2022)http://hdl.handle.net/11420/10925We derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator ∂ between spaces of weighted smooth Fréchet-valued functions. This is done by establishing an analog of Hörmander's theorem on the solvability of the inhomogeneous Cauchy-Riemann equation in a space of smooth ℂ-valued functions whose topologyis given by a whole family of weights. Our proof relies on a weakened variant of weak reducibility of the corresponding subspace of holomorphic functions in combination with the Mittag-Leffler procedure. Using tensor products, we deduce the corresponding result on the solvability of the inhomogeneous Cauchy-Riemann equation for Fréchet-valued functions.en1747-69412022132Taylor & Francis32W0535A0146A3246E40Cauchy–RiemannFréchetsmoothsolvabilitysurjectiveweightMathematics - Functional AnalysisMathematics - Functional Analysis35A01, 32W05, 46A32, 46E40MathematikJournal Article10.1080/17476933.2021.19455871810.05069v2Other