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

Abstract

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