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Harmonic functions, conjugate harmonic functions and the Hardy space H1 in the rational Dunkl setting

Abstract : In this work we extend the theory of the classical Hardy space H 1 to the rational Dunkl setting. Specifically, let ∆ be the Dunkl Laplacian on a Euclidean space R N. On the half-space R + ×R N , we consider systems of conjugate (∂ 2 t +∆ x)-harmonic functions satisfying an appropriate uniform L 1 condition. We prove that the boundary values of such harmonic functions, which constitute the real Hardy space H 1 ∆ , can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or Littlewood-Paley square functions.
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Contributor : Jean-Philippe Anker <>
Submitted on : Saturday, November 17, 2018 - 10:07:29 AM
Last modification on : Monday, May 6, 2019 - 10:28:08 AM
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Jean-Philippe Anker, Jacek Dziubanski, Agnieszka Hejna. Harmonic functions, conjugate harmonic functions and the Hardy space H1 in the rational Dunkl setting. Journal of Fourier Analysis and Applications, Springer Verlag, 2019. ⟨hal-01925688⟩

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