New Calderon reproducing formulae with exponential decay on spaces of homogeneous type
New Calderon reproducing formulae with exponential decay on spaces of homogeneous type
复制标题
新卡尔德隆在齐次类型空间上再现指数衰减公式
DOI：
10.1007/s11425-018-9346-4
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Yuan Wen
中科院分区：
文献类型：
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作者：
He Ziyi;Liu Liguang;Yang Dachun;Yuan Wen
假设(X，d，μ)是Coifman和Weiss(1971,1977)意义下的齐型空间。本文受Auscher和Hytönen(2013)关于齐型空间上正则小波正交基的突破性工作的启发，引入了一种新的指数衰减恒等式的逼近(简称EXP-ATI)。在韩等人的另一个创造性想法的推动下，通过这样的实验-ATI。(2018)为了将上述正则小波正交基合并到齐型空间上已有的分布理论的框架中，我们建立了(X，d，μ)上的齐次连续/离散Calderón再生公式，以及它们的非齐次对应公式。这篇文章的新奇之处在于，d只被假设为准度量，而基础度量μ是加倍度量，而不是满足反向加倍条件所必需的。众所周知，Calderón再生公式是发展分析的基石，特别是齐型空间上的调和分析。
Assume that (X, d, μ) is a space of homogeneous type in the sense of Coifman and Weiss (1971, 1977). In this article, motivated by the breakthrough work of Auscher and Hytönen (2013) on orthonormal bases of regular wavelets on spaces of homogeneous type, we introduce a new kind of approximations of the identity with exponential decay (for short, exp-ATI). Via such an exp-ATI, motivated by another creative idea of Han et al. (2018) to merge the aforementioned orthonormal bases of regular wavelets into the frame of the existed distributional theory on spaces of homogeneous type, we establish the homogeneous continuous/discrete Calderón reproducing formulae on (X, d, μ), as well as their inhomogeneous counterparts. The novelty of this article exists in that d is only assumed to be a quasi-metric and the underlying measureμa doubling measure, not necessary to satisfy the reverse doubling condition. It is well known that Calderón reproducing formulae are the cornerstone to develop analysis and, especially, harmonic analysis on spaces of homogeneous type.