New John–Nirenberg–Campanato‐type spaces related to both maximal functions and their commutators

Abstract

Let p,q-1pt∈-1ptfalse[1,∞false], α∈ℝ, and s be a nonnegative integer. In this article, the authors introduce a new function space trueJN˜false(p,q,sfalse)αfalse(scriptXfalse) of John–Nirenberg–Campanato type, where scriptX denotes ℝn or any cube Q0 of ℝn with finite edge length. The authors give an equivalent characterization of trueJN˜false(p,q,sfalse)αfalse(scriptXfalse) via both the John–Nirenberg–Campanato space and the Riesz–Morrey space. Moreover, for the particular case s=0, this new space can be equivalently characterized by both maximal functions and their commutators. Additionally, the authors give some basic properties, a good‐ λ inequality, and a John–Nirenberg‐type inequality for trueJN˜false(p,q,sfalse)αfalse(scriptXfalse).