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

Pavlović, Miroslav. "A formula for the Bloch norm of a $C^1$-function on the unit ball of $\mathbb {C}^n$." Czechoslovak Mathematical Journal 58.4 (2008): 1039-1043. <http://eudml.org/doc/37883>.

@article{Pavlović2008,
abstract = {For a $C^1$-function $f$ on the unit ball $\mathbb \{B\} \subset \mathbb \{C\} ^n$ we define the Bloch norm by $\Vert f\Vert _\mathfrak \{B\}=\sup \Vert \tilde\{d\}f\Vert ,$ where $\tilde\{d\}f$ is the invariant derivative of $f,$ and then show that \[ \Vert f\Vert \_\mathfrak \{B\}= \sup \_\{z,w\in \{\mathbb \{B\}\} \atop z\ne w\} (1-|z|^2)^\{1/2\}(1-|w|^2)^\{1/2\}\frac\{|f(z)-f(w)|\}\{|w-P\_wz-s\_wQ\_wz|\}.\]},
author = {Pavlović, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bloch norm; Möbius transformation; Bloch norm; Möbius transformation},
language = {eng},
number = {4},
pages = {1039-1043},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A formula for the Bloch norm of a $C^1$-function on the unit ball of $\mathbb \{C\}^n$},
url = {http://eudml.org/doc/37883},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Pavlović, Miroslav
TI - A formula for the Bloch norm of a $C^1$-function on the unit ball of $\mathbb {C}^n$
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1039
EP - 1043
AB - For a $C^1$-function $f$ on the unit ball $\mathbb {B} \subset \mathbb {C} ^n$ we define the Bloch norm by $\Vert f\Vert _\mathfrak {B}=\sup \Vert \tilde{d}f\Vert ,$ where $\tilde{d}f$ is the invariant derivative of $f,$ and then show that \[ \Vert f\Vert _\mathfrak {B}= \sup _{z,w\in {\mathbb {B}} \atop z\ne w} (1-|z|^2)^{1/2}(1-|w|^2)^{1/2}\frac{|f(z)-f(w)|}{|w-P_wz-s_wQ_wz|}.\]
LA - eng
KW - Bloch norm; Möbius transformation; Bloch norm; Möbius transformation
UR - http://eudml.org/doc/37883
ER -