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

Jean-Philippe Anker (1) , Jacek Dziubanski (2) , Agnieszka Hejna (3)

1 IDP - Institut Denis Poisson
2 Instytut Matematyczny
3 Instytut Matematyczny

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.

Domaines: Mathématiques [math]; Analyse fonctionnelle [math.FA]

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⟩