Surjectivity of the ∂-operator between weighted spaces of smooth vector-valued functions

Publikationstyp
Journal Article
Publikationsdatum
2022
Sprache
English
Author
Kruse, Karsten 
Institut
Mathematik E-10 
TORE-URI
http://hdl.handle.net/11420/10925
Enthalten in
Complex variables and elliptic equations 
Start Page
1
End Page
32
Article Number
1945587
Citation
Complex Variables and Elliptic Equations 67: 2676 - 2707 (2022)
Publisher DOI
10.1080/17476933.2021.1945587
Scopus ID
2-s2.0-85109318405
ArXiv ID
1810.05069v2
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.
Schlagworte
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