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

Abstract

Let , , and be a nonnegative integer. In this article, the authors introduce a new function space of John–Nirenberg–Campanato type, where denotes or any cube of with finite edge length. The authors give an equivalent characterization of via both the John–Nirenberg–Campanato space and the Riesz–Morrey space. Moreover, for the particular case , this new space can be equivalently characterized by both maximal functions and their commutators. Additionally, the authors give some basic properties, a good‐ inequality, and a John–Nirenberg‐type inequality for .