Intrinsic Square Function Characterizations of Variable Hardy–Lorentz Spaces

Abstract

The aim of this paper is to establish the intrinsic square function characterizations in terms of the intrinsic Littlewood–Paleyg-function, the intrinsic Lusin area function, and the intrinsicgλ∗-function of the variable Hardy–Lorentz spaceHp⋅,qℝn, forp⋅being a measurable function onℝnsatisfying0<p−≔ess infx∈ℝnpx≤ess supx∈ℝnpx≕p+<∞and the globally log-Hölder continuity condition andq∈0,∞, via its atomic and Littlewood–Paley function characterizations.