论文标题
新约翰 - 尼伦贝格 - 坎帕纳托型空间与最大功能及其换向器有关
New John--Nirenberg--Campanato-Type Spaces Related to Both Maximal Functions and Their Commutators
论文作者
论文摘要
令$ p，q \ in [1，\ infty] $，$α\ in {\ mathbb {r}} $，而$ s $为非负整数。在本文中，作者介绍了一个新的功能空间$ \ widetilde {Jn} _ {（p，q，q，s）_α}（\ john-nirenberg-campanato类型的\ Mathcal {x}）$ $ \ mathbb {r}^n $，具有有限的边缘长度。作者通过John-Nirenberg-campanato Space和Riesz-Morrey Space提供了$ \ widetilde {Jn} _ {（p，q，q，s）_α} $的等效表征。此外，对于特定情况$ s = 0 $，这个新空间可以等效地以最大功能及其换向器为特征。此外，作者提供了一些基本的属性，$ $λ$不等式，而约翰 - 尼伦贝格类型的不平等等于$ \ widetilde {jn} _ {（p，q，q，s）_α}（\ nathcal {x}）$。
Let $p,q\in [1,\infty]$, $α\in{\mathbb{R}}$, and $s$ be a non-negative integer. In this article, the authors introduce a new function space $\widetilde{JN}_{(p,q,s)_α}(\mathcal{X})$ of John-Nirenberg-Campanato type, where $\mathcal{X}$ denotes $\mathbb{R}^n$ or any cube $Q_{0}$ of $\mathbb{R}^n$ with finite edge length. The authors give an equivalent characterization of $\widetilde{JN}_{(p,q,s)_α}(\mathcal{X})$ 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 $\widetilde{JN}_{(p,q,s)_α}(\mathcal{X})$.
