Criteria of a Two-Weight, Weak-Type Inequality in Orlicz Classes for Maximal Functions Defined on Homogeneous Spaces

Abstract

In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form φ1(λ)∫{x∈X:Mf(x)>λ}ϱ(x)dμ(x)≤c∫Xφ2c|f(x)|σ(x)dμ(x) are obtained in Orlicz classes, where Mf is a Hardy–Littlewood maximal function defined on homogeneous spaces and ϱ is a weight function.

Keywords

• weight
• weak-type inequality
• Hardy–Littlewood maximal function
• Orlicz classes