On Weyl multipliers for unconditional convergence of series in Ciesielski systems

We prove that a nondecreasing sequence of positive numbers $\omega_n$ is a Weyl multiplier for the almost everywhere unconditional convergence of series in Ciesielski systems if and only if the inequality $\sum_{n=1}^{\infty}(n\omega_n)^{-1}<\infty$ holds.