The $\bar\partial$-Neumann operator and commutators of the Bergman projection and multiplication operators

Title:

The $\bar\partial$-Neumann operator and commutators of the Bergman projection and multiplication operators

Creator:

Haslinger, Friedrich

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8151de8d-4885-47da-8ad4-313255182b24
uuid:8151de8d-4885-47da-8ad4-313255182b24

Subject:

$\bar{\partial}$-equation, $\bar{\partial}$-Neumann operator, and compactness

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We prove that compactness of the canonical solution operator to $\bar \partial $ restricted to $(0,1)$-forms with holomorphic coefficients is equivalent to compactness of the commutator $[\mathcal P,\bar M]$ defined on the whole $L^2_{(0,1)}(\Omega ),$ where $\bar M$ is the multiplication by $\bar z$ and $\mathcal P $ is the orthogonal projection of $L^2_{(0,1)}(\Omega )$ to the subspace of $(0,1)$ forms with holomorphic coefficients. Further we derive a formula for the $\bar \partial $-Neumann operator restricted to $(0,1)$ forms with holomorphic coefficients expressed by commutators of the Bergman projection and the multiplications operators by $z $ and $\bar z$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1247-1256

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:4

Harvested from:

CDK

Metadata only:

false