This paper is perhaps the first attempt at a study of the Hardy space H 1 in the rational Dunkl setting. Following Uchiyama's approach, we characterize H 1 atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for H 1 . These results are proved here in the one-dimensional case and in the product case.

In this paper, a product formula for the eigenfunction of the Jacobi-Dunkl differential-difference operator is derived. It leads to a uniformly bounded convolution of point measures and a signed hypergroup on IR.

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