论文标题
BMO和John-Nirenberg的不平等现象
BMO and the John-Nirenberg Inequality on Measure Spaces
论文作者
论文摘要
我们研究了一个测量空间$ \ mathbb {x} $的一般设置中的空间BMO，并具有固定的集合$ \ Mathscr {g} $的可测量的正面和有限度量集，由$ \ m vasterscr {g} $组成的有限均值振荡函数。目的是查看熟悉的BMO机械在公制概念被测为理论替换时所拥有的。特别是，考虑到BMO的三个方面：它作为Banach空间的特性，与Muckenhoupt重量的关系以及John-Nirenberg的不平等。我们为BMO成为Banach Space Modulo常数提供了可分解的度量空间$ \ MATHBB {X} $的必要条件。我们还开发了Denjoy家族$ \ MATHSCR {G} $的概念，该$保证BMO中的功能满足了John-Nirenberg的不平等，这对$ \ Mathscr {g} $的元素。
We study the space BMO in the general setting of a measure space $\mathbb{X}$ with a fixed collection $\mathscr{G}$ of measurable sets of positive and finite measure, consisting of functions of bounded mean oscillation on sets in $\mathscr{G}$. The aim is to see how much of the familiar BMO machinery holds when metric notions have been replaced by measure-theoretic ones. In particular, three aspects of BMO are considered: its properties as a Banach space, its relation with Muckenhoupt weights, and the John-Nirenberg inequality. We give necessary and sufficient conditions on a decomposable measure space $\mathbb{X}$ for BMO to be a Banach space modulo constants. We also develop the notion of a Denjoy family $\mathscr{G}$, which guarantees that functions in BMO satisfy the John-Nirenberg inequality on the elements of $\mathscr{G}$.
