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Hardy spaces for the Dunkl harmonic oscillator
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2020-08-09 , DOI: 10.1002/mana.201900215
Agnieszka Hejna 1
Affiliation  

Let $\Delta$ and $L=\Delta -\|\mathbf x\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup $e^{tL}$. We prove that the space $\mathcal H^1$ admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic decompositions are of local type.

中文翻译:

Dunkl 谐振子的 Hardy 空间

令 $\Delta$ 和 $L=\Delta -\|\mathbf x\|^2$ 分别为 Dunkl Laplacian 和 Dunkl 谐振子。我们通过相对于半群 $e^{tL}$ 的非切向极大函数来定义与 Dunkl 谐振子相关的 Hardy 空间 $\mathcal H^1$。我们证明空间 $\mathcal H^1$ 承认相关 Riesz 变换和原子分解的表征。原子分解中出现的原子是局部类型的。
更新日期:2020-08-09
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