  We prove that the homogeneous functional calculus associated to $x\mapsto
|x|^\theta$ or $x\mapsto {\rm sgn}\, (x) |x|^{\theta}$ for $0<\theta<1$ is
$\theta$-H\"older on selfadjoint elements of noncommutative $L_p$-spaces for
$0<p\leq\infty$ with values in $L_{p/\theta}$. This extends an inequality of
Birman, Koplienko and Solomjak also obtained by Ando.
