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

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

Publikationstyp

Journal Article

Publikationsdatum

2022

Sprache

English

Author

Kruse, Karsten

Institut

Enthalten in

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.