Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2019

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

Jacek Dziubanski
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Agnieszka Hejna
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Résumé

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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DOI

Cite 10.1007/s00041-019-09666-0 Autre Anker, J.-P., Dziubański, J., & Hejna, A. (2019). Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space $$H^1$$ H 1 in the Rational Dunkl Setting. Journal of Fourier Analysis and Applications, 25(5), 2356–2418. https://doi.org/10.1007/s00041-019-09666-0

Dates et versions

hal-01925688 , version 1 (17-11-2018)

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  • HAL Id : hal-01925688 , version 1

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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, 2019. ⟨hal-01925688⟩
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