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We devote this note to correct an estimate concerning mixed inequalities forthe generalized maximal function $M_\Phi$, when certain properties of theassociated Young function $\Phi$ are assumed.  Although the obtained estimates turn out to be slightly different, they aregood extensions of mixed inequalities for the classical Hardy-Littlewoodmaximal functions $M_r$, with $r\geq 1$. They also allow us to obtain mixedestimates for the generalized fractional maximal operator $M_{\gamma,\Phi}$,when $0<\gamma<n$ and $\Phi$ is an $L\log L$ type function.

Corrgiendum to "From $A_1$ to $A_\infty$: new mixed inequalities for certain maximal operators''