A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$

Title:

A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$

Creator:

Pavlović, Miroslav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:4d2fc20b-7953-4139-bd24-5b4dd8a07831
uuid:4d2fc20b-7953-4139-bd24-5b4dd8a07831

Subject:

Bloch norm and Möbius transformation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For a $C^1$-function $f$ on the unit ball $\mathbb B \subset \mathbb C ^n$ we define the Bloch norm by $\|f\|_\mathfrak B=\sup \|\tilde df\|,$ where $\tilde df$ is the invariant derivative of $f,$ and then show that $$ \|f\|_\mathfrak B= \sup _{z,w\in {\mathbb B} \atop z\neq w} (1-|z|^2)^{1/2}(1-|w|^2)^{1/2}\frac {|f(z)-f(w)|}{|w-P_wz-s_wQ_wz|}.$$.

Language:

English

Rights:

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

Coverage:

1039-1043

Source:

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

Harvested from:

CDK

Metadata only:

false