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Hardy spaces for the Dunkl harmonic oscillator

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  • Agnieszka Hejna

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.

Suggested Citation

  • Agnieszka Hejna, 2020. "Hardy spaces for the Dunkl harmonic oscillator," Mathematische Nachrichten, Wiley Blackwell, vol. 293(11), pages 2112-2139, November.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:11:p:2112-2139
    DOI: 10.1002/mana.201900215
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