论文标题
稀疏统治的公制方法
A metric approach to sparse domination
论文作者
论文摘要
我们提出了一种基于单尺度$ l^p $提示作为关键属性的稀疏支配的通用方法。结果是在均匀类型的度量空间的设置中提出的，并避免完全使用二元 - 良好技术以及Christ-Hytönen-Kairema Cubes。在我们的一般原则的应用中，我们恢复了二连续的calderón-zygmund内核在同质类型的空间上稀疏的统治，我们证明了一个稀疏界限的家庭，用于与表现出傅立叶衰变相关的最大函数相关的最大功能，我们推出了稀疏的radon transpares in polynomial submanifolds $ n $ nifd n $ under sup manifolds $ n n $^n n f. n。
We present a general approach to sparse domination based on single-scale $L^p$-improving as a key property. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ-Hytönen-Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón-Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of $\mathbb R^n$.
