Semigroup and Riesz transform for the Dunkl- Schrödinger operators

2019/10/14 by Amri, Béchir, Hammi, Amel
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1910.06245

Abstract

Let L_k=-Δ_k+V be the Dunk- Schrödinger operators, where Δ_k=∑_j=1^dT_j² is the Dunkl Laplace operator associated to the dunkl operators T_j on ℝ^d and V is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform R_j= T_j L_k^-1/2 as an L²- bounded operator and we prove that is of weak type (1,1) and then is bounded on L^p(ℝ^d,dμ_k(x)) for 1

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