Potential operators and laplace type multipliers associated with the twisted laplacian

We study potential operators and, more generally, Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian. We characterize those 1 ≤ p,q ≤ ∞, for which the potential operators are L^p – L^q bounded. This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions. We also investigate L^p mapping properties of the Laplace-Stieltjes and Laplace type multipliers.