Geodesic
A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1039-1043 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $$ \|f\|_\mathfrak B= \sup _{z,w\in {\mathbb B} \atop z\neq w} (1-|z|^2)^{1/2}(1-|w|^2)^{1/2}\frac {|f(z)-f(w)|}{|w-P_wz-s_wQ_wz|}.$$
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 $$ \|f\|_\mathfrak B= \sup _{z,w\in {\mathbb B} \atop z\neq w} (1-|z|^2)^{1/2}(1-|w|^2)^{1/2}\frac {|f(z)-f(w)|}{|w-P_wz-s_wQ_wz|}.$$
Classification : 30D45, 32A18, 32A37, 46E15
Keywords: Bloch norm; Möbius transformation 
@article{CMJ_2008_58_4_a10,
     author = {Pavlovi\'c, Miroslav},
     title = {A formula for the {Bloch} norm of a $C^1$-function on the unit ball of $\Bbb C^n$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1039--1043},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471163},
     zbl = {1174.32003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a10/}
}
TY  - JOUR
AU  - Pavlović, Miroslav
TI  - A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 1039
EP  - 1043
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a10/
LA  - en
ID  - CMJ_2008_58_4_a10
ER  - 
%0 Journal Article
%A Pavlović, Miroslav
%T A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$
%J Czechoslovak Mathematical Journal
%D 2008
%P 1039-1043
%V 58
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a10/
%G en
%F CMJ_2008_58_4_a10
Pavlović, Miroslav. A formula for the Bloch norm of a $C^1$-function on the unit ball of $\Bbb C^n$. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1039-1043. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a10/