For a $C^1$-function $f$ on the unit ball $𝔹\subset {ℂ}^n$ we define the Bloch norm by ${\parallel f\parallel }_{𝔅}=sup\parallel \tilde{d}f\parallel ,$ where $\tilde{d}f$ is the invariant derivative of $f,$ and then show that $${\parallel f\parallel }_{𝔅}=\underset{\genfrac{}{}{0pt}{}{z,w\in 𝔹}{z\ne w}}{sup}{(1-|z|}^2{)}^{1/2}{(1-|w|}^2{)}^{1/2}\frac{\left|f\right(z)-f(w\left)\right|}{|w-P_{w}z-s_w{Q}_{w}z|}.$$

In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space $bmo{(}^N)$ of functions of bounded mean oscillation is a strict subspace of the mean little BMO.