论文标题
定量约翰·尼伦贝格（John-Nirenberg）的不平等现象
Quantitative John-Nirenberg inequalities at different scales
论文作者
论文摘要
我们提供了表格的抽象估计\ [ \ | f-f_ {q，μ} \ | _ {x \ left（q，\ frac {\ mathrm {d}μ} {y（q）} \ right）} \ leq c（μ） \ \]对于所有立方体，$ \ Mathbb {r}^n $和每个功能$ f \ in \ mathrm {bmo}（\ Mathrm {d}μ）$，其中$μ$是$ \ alsbb {r}^n $，$ y $ y Mathbb {r}^n $，$ y $的倍增度，是$ \ y $ y $ y $ y $ cy \ y \ cy \ cudy | cus y | \ left（q，\ frac {\ mathrm {d} w} {w（q）} \ right）} $是一个足够好的准准分子，$ c（μ，y）$和$ψ（x）$是正值的，分别取决于$μ$和$ y $，以及$ y $，以及$ x $。该抽象方案使我们能够恢复尖锐的估计\ [ \ | f-f_ {q，μ} \ | _ {l^p \ left（q，q，\ frac {\ mathrm {d}μ（x）} {μ（q）} \ right）} \ leq c（q）} \ leq c（μ） \ qquad p \ geq1 \]对于每个立方体$ q $和\ mathrm {bmo}（\ mathrm {d}μ）$中的每个$ f \ in \ qquad p \ geq1 \] $等同于约翰 - 尼伦贝格的不平等，也使我们能够获得$ l^p $ replative＆replative＆reppers＆quofe l^p $，并且在$ like po p $ po $时，$ f \ quq1 \ geq1 \]。 $ l^{p（\ cdot）} $ spaces。 除了上述结果，我们还将[OPRRR20]中的定理1.2推广到倍增度量的设置，并获得了Muckenhoupt的$ a_ \ iftty $ striges的新表征。
We provide an abstract estimate of the form \[ \|f-f_{Q,μ}\|_{X \left(Q,\frac{\mathrm{d} μ}{Y(Q)}\right)}\leq c(μ,Y)ψ(X)\|f\|_{\mathrm{BMO}(\mathrm{d}μ)} \] for all cubes $Q$ in $\mathbb{R}^n$ and every function $f\in \mathrm{BMO}(\mathrm{d}μ)$, where $μ$ is a doubling measure in $\mathbb{R}^n$, $Y$ is some positive functional defined on cubes, $\|\cdot \|_{X \left(Q,\frac{\mathrm{d} w}{w(Q)}\right)}$ is a sufficiently good quasi-norm and $c(μ,Y)$ and $ψ(X)$ are positive constants depending on $μ$ and $Y$, and $X$, respectively. That abstract scheme allows us to recover the sharp estimate \[ \|f-f_{Q,μ}\|_{L^p \left(Q,\frac{\mathrm{d} μ(x)}{μ(Q)}\right)}\leq c(μ)p\|f\|_{\mathrm{BMO}(\mathrm{d}μ)}, \qquad p\geq1 \] for every cube $Q$ and every $f\in \mathrm{BMO}(\mathrm{d}μ)$, which is known to be equivalent to the John-Nirenberg inequality, and also enables us to obtain quantitative counterparts when $L^p$ is replaced by suitable strong and weak Orlicz spaces and $L^{p(\cdot)}$ spaces. Besides the aforementioned results we also generalize Theorem 1.2 in [OPRRR20] to the setting of doubling measures and obtain a new characterization of Muckenhoupt's $A_\infty$ weights.
