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
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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 
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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/

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