An abstract Coifman-Rochberg-Weiss commutator theorem

Dunkl 框架中的 $H^p$ 空间与 Coifman--Weiss 型原子

$H^p$ spaces in the Dunkl setting meet Coifman--Weiss--type atoms

针对任意根系与非负重函数的Dunkl拉普拉斯算子，建立了Hardy空间H^p的Coifman-Weiss型原子刻画，证明其与满足消没条件的原子生成空间一致，并给出拟范数等价及L^∞尺寸条件的等价性。

A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type

Let $(X,d,μ)$ be a space of homogeneous type, with the upper dimension $ω$, in the sense of R. R. Coifman and G. Weiss. Assume that $η$ is the smoothness index of the wavelets on $X$ constructed by P. Auscher and T. Hytönen. In this article, when $p\in(ω/(ω+η),1]$, for the atomic Hardy spaces $H_{\mathrm{cw}}^p(X)$ introduced by Coifman and Weiss, the authors establish their various real-variable characterizations, respectively, in terms of the grand maximal function, the radial maximal function, the non-tangential maximal functions, the various Littlewood-Paley functions and wavelet functions…

Radial Maximal Function Characterizations of Hardy Spaces on RD-Spaces and Their Applications

Let ${\mathcal X}$ be an RD-space with $μ({\mathcal X})=\infty$, which means that ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we characterize the atomic Hardy spaces $H^p_{\rm at}(\{\mathcal X})$ of Coifman and Weiss for $p\in(n/(n+1),1]$ via the radial maximal function, where $n$ is the "dimension" of ${\mathcal X}$, and the range of index $p$ is the best possible. This completely answers the question proposed by Ronald R. Coifman and Guido Weiss in 1977 in this setting, and improves on a dee…

Real-Variable Characterizations of Local Hardy Spaces on Spaces of Homogeneous Type

Suppose that $(X,d,μ)$ is a space of homogeneous type, with upper dimension $μ$, in the sense of R. R. Coifman and G. Weiss. Let $η$ be the Hölder regularity index of wavelets constructed by P. Auscher and T. Hytönen. In this article, the authors introduce the local Hardy space $h^{*,p}(X)$ via local grand maximal functions and also characterize $h^{*,p}(X)$ via local radial maximal functions, local non-tangential maximal functions, locally atoms and local Littlewood--Paley functions. Furthermore, the authors establish the relationship between the global and the local Hardy spaces. Finally, th…