Riesz potentials of Radon measures associated to reflection groups

For a root system R on R-d and a nonnegative multiplicity function k on R, we consider the heat kernel p(k)(t, x, y) associated to the Dunkl Laplacian operator Delta(k). For beta epsilon]0, d + 2y [, where y = 1/2 Sigma(alpha epsilon R) k(alpha), we study the Delta(k)- Riesz kernel of index beta, defined by R-k,R- beta (x, y) = 1/Gamma(beta/2)integral(+infinity)(0) t(beta/2-1) pk (t, x, y) dt, and the corresponding Delta(k)- Riesz potential I-k, beta[mu] of a Radon measure mu on R d. According to the values of beta, we study the Delta(k)- superharmonicity of these functions, and we give some applications like the Delta(k)- Riesz measure of I-k, beta [mu], the uniqueness principle and a pointwise Hedberg inequality.