On absolute values of QK functions

In this paper, the effect of absolute values on the behavior of functions $f$ in the spaces ${\mathcal{Q}}_K$ is investigated. It is clear that $f\in $\mathcal{Q}$_K(\partial {$\mathbb{D}$}) \Rightarrow |f|\in $\mathcal{Q}$_K(\partial {$\mathbb{D}$})$,buttheconverseisnotalwaystrue\mathrm{.}For$f$intheHardyspace$H^2$, we give a condition involving the modulus of the function only, such that this condition together with $\mathrm{\mid }f\mathrm{\mid }\in {\mathcal{Q}}_K(\mathrm{\partial }\mathbb{D})$ is equivalent to $f\in {\mathcal{Q}}_K$. As an application, a new criterion for inner-outer factorisation of ${\mathcal{Q}}_K$ spaces is given. These results are also new for ${\mathcal{Q}}_p$ spaces.