论文标题
未列出最大函数在度量测量空间上的下限
Lower bounds for uncentered maximal functions on metric measure space
论文作者
论文摘要
我们表明，$ \ mathbb {r}^d $在$ \ mathbb {r}^d $上与ra量$ $ $ $ $相关的无用的硬木最大运算符具有统一的均匀$ l^p $ bug bug bug-bounds（与$μ$相关），严格大于$ 1 $，如果$ 1 $ $ 1 $，如果$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ unfus uff $ \ f \}实际上，我们在公制量度空间$（x，d，μ）的更一般环境中这样做，满足了Besicovitch覆盖属性。此外，我们还说明，构造反例无法忽略连续性条件。
We show that the uncentered Hardy-Littlewood maximal operators associated with the Radon measure $μ$ on $\mathbb{R}^d$ have the uniform lower $L^p$-bounds (independent of $μ$) that are strictly greater than $1$, if $μ$ satisfies a mild continuity assumption and $μ(\mathbb{R}^d)=\infty$. We actually do that in the more general context of metric measure space $(X,d,μ)$ satisfying the Besicovitch covering property. In addition, we also illustrate that the continuity condition can not be ignored by constructing counterexamples.
