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Let ω be a Békollé-Bonami weight. We give a complete characterization of the positive measures μ such that ${\int }_{}|M_{\omega }{f\left(z\right)|}^{q}d\mu \left(z\right)\le C({\int }_{}{\left|f\left(z\right)\right|}^p{\omega \left(z\right)dV\left(z\right))}^{q/p}$ and $\mu \left(z\in :Mf\left(z\right)>\lambda \right)\le C/\left({\lambda }^q\right)({\int }_{}|f\left(z\right){{|}^p\omega \left(z\right)dV\left(z\right))}^{q/p}$, where $M_{\omega }$ is the weighted Hardy-Littlewood maximal function on the upper half-plane and 1 ≤ p,q <; ∞.