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arXiv · 1802.08518

Hardy spaces for the Dunkl harmonic oscillator

Agnieszka Hejna
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Abstract

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.

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Agnieszka Hejna. 2018-02-23. Hardy spaces for the Dunkl harmonic oscillator. https://arxiv.org/abs/1802.08518

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