Corrigendum 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 $M_\Phi$ given in Berra (Potential Anal. 57(1), 1–27, 2022), 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 $r\ge 1$. 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.