Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space H1 in the Rational Dunkl Setting

In this work we extend the theory of the classical Hardy space H-1 to the rational Dunkl setting. Specifically, let Delta be the Dunkl Laplacian on a Euclidean space R-N. On the half-space R+ x R-N, we consider systems of conjugate (partial derivative(2)(t) + Delta(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-Delta(1), can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or Littlewood-Paley square functions.