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: | 2022 | Verlag: | Taylor & Francis | Quellenangabe: | Complex Variables and Elliptic Equations 67: 2676 - 2707 (2022) | 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 |
Enthalten in den Sammlungen: | Publications without fulltext |
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