Verlagslink DOI: 10.1080/17476933.2021.1945587
arXiv ID: 1810.05069v2
Titel: Surjectivity of the ∂-operator between weighted spaces of smooth vector-valued functions
Sprache: Englisch
Autor/Autorin: Kruse, Karsten  
Schlagwörter: 32W05; 35A01; 46A32; 46E40; Cauchy–Riemann; Fréchet; smooth; solvability; surjective; weight; Mathematics - Functional Analysis; Mathematics - Functional Analysis; 35A01, 32W05, 46A32, 46E40
Erscheinungs­datum: 30-Jun-2021
Verlag: Taylor & Francis
Quellenangabe: Complex Variables and Elliptic Equations : 1945587 (2021) (in press; CC BY 4.0)
Zusammenfassung (englisch): 
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.
URI: http://hdl.handle.net/11420/10925
ISSN: 1747-6941
Zeitschrift: Complex variables and elliptic equations 
Institut: Mathematik E-10 
Dokumenttyp: Artikel/Aufsatz
Peer Reviewed: Ja
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