Triebel-Lizorkin spaces in Dunkl setting

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-30 DOI:arxiv-2408.05227

Chuhan Sun, Zhiming Wang

引用次数: 0

Abstract

We establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric. In this paper, the L^2 space and the Dunkl-Calderon-Zygmund singular integral operator in the Dunkl setting play a fundamental role. The main tools used in this paper are as follows: (i) the Dunkl-Calder\'on-Zygmund singular integral operator and a new Calderon reproducing formula in L^2 with the Triebel-Lizorkin space norms; (ii) new test functions in terms of the \L^2 functions and distributions; (iii) the Triebel-Lizorkin spaces in the Dunkl setting which are defined by the wavelet-type decomposition with norms and the analogous atomic decomposition of the Hardy spaces.

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邓克尔背景下的特里贝尔-利佐尔金空间

我们在 Dunkl 设置中建立了与欧几里得空间上的有限反射群相关联的 Triebel-Lizorkin 空间。群结构诱导出两种非等价度量：欧几里得度量和邓克尔度量。在本文中，L^2 空间和邓克尔背景下的邓克尔-卡尔德隆-齐格蒙奇异积分算子起着基本作用。本文使用的主要工具如下：(i) Dunkl-Calder\'on-Zygmund 奇异积分算子和 L^2 中带有 Triebel-Lizorkin 空间规范的新 Calderon 重现公式；(ii) 用 \L^2 函数和分布表示的新检验函数；(iii) Dunklsetting 中的 Triebel-Lizorkin 空间，这些空间由带有规范的小波型分解和 Hardy 空间的类似原子分解定义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Classical Analysis and ODEs

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