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