Publisher DOI: 10.1080/17476933.2021.1945587
arXiv ID: 1810.05069v2
Title: Surjectivity of the ∂-operator between weighted spaces of smooth vector-valued functions
Language: English
Authors: Kruse, Karsten  
Keywords: 32W05;35A01;46A32;46E40;Cauchy–Riemann;Fréchet;smooth;solvability;surjective;weight;Mathematics - Functional Analysis;Mathematics - Functional Analysis;35A01, 32W05, 46A32, 46E40
Issue Date: 30-Jun-2021
Publisher: Taylor & Francis
Source: Complex Variables and Elliptic Equations : 1945587 (2021) (in press; CC BY 4.0)
Abstract (english): 
We 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.
ISSN: 1747-6941
Institute: Mathematik E-10 
Document Type: Article
Peer Reviewed: Yes
Journal: Complex variables and elliptic equations 
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