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Surjectivity of the ∂-operator between weighted spaces of smooth vector-valued functions
Publikationstyp
Journal Article
Date Issued
2022
Sprache
English
Author(s)
Institut
Start Page
1
End Page
32
Article Number
1945587
Citation
Complex Variables and Elliptic Equations 67: 2676 - 2707 (2022)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Taylor & Francis
Peer Reviewed
true
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.
Subjects
32W05
35A01
46A32
46E40
Cauchy–Riemann
Fréchet
smooth
solvability
surjective
weight
Mathematics - Functional Analysis
Mathematics - Functional Analysis
35A01, 32W05, 46A32, 46E40
DDC Class
510: Mathematik