Hardy spaces for the Dunkl harmonic oscillator

Agnieszka Hejna

Mathematische Nachrichten, 2020, vol. 293, issue 11, 2112-2139

Abstract: Let Δ and L=Δ−∥x∥2 be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup etL. We prove that the space H1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic decompositions are of local type.

Date: 2020
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https://doi.org/10.1002/mana.201900215

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