### Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class

We collect known and prove new necessary and sufficient conditions for the weighted weak type maximal inequality of the form $${\Phi}_{1}\left(\lambda \right)\varrho \left(\{x\in X:{M}_{\mu}f\left(x\right)>\lambda \}\right)\le c{\int}_{X}{\Phi}_{2}\left(c\right|f\left(x\right)\left|\right)\sigma \left(x\right)\mathrm{d}\mu \left(x\right),$$ which extends some known results.