  We study potential operators associated with Laguerre function expansions of
convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove
qualitatively sharp estimates of the corresponding potential kernels. Then we
characterize those $1 \le p,q \le \infty$, for which the potential operators
are $L^p-L^q$ bounded. These results are sharp analogues of the classical
Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and
Dunkl-Laguerre settings.
