Corrigendum to “From $$A_1$$ to $$A_\infty $$ : New Mixed Inequalities for Certain Maximal Operators”

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-07-10 DOI:10.1007/s11118-023-10088-3

Fabio Berra

引用次数: 0

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.

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“从$$A_1$$到$$A_\infty $$:某些极大算子的新混合不等式”的勘误表

当相关Young函数$\Phi $的某些性质被假设时，我们将此注释用于修正Berra (Potential Anal. 57(1)， 1 - 27,2022)中给出的关于广义极大函数$M_\Phi $的混合不等式的估计。虽然得到的估计结果略有不同，但它们是经典Hardy-Littlewood极大函数$M_r$的混合不等式的良好扩展，其中$r\ge 1$。它们还允许我们获得广义分数极大算子$M_{\gamma ,\Phi }$的混合估计，当$0<\gamma <n$和$\Phi $是$L\log L$类型函数时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.