  In this paper, we obtain the weighted boundedness for the local
multi(sub)linear Hardy-Littlewood maximal operators and local multilinear
fractional integral operators associated with the local Muckenhoupt weights on
Gaussian measure spaces. We deal with these problems by introducing a new
pointwise equivalent "radial" definitions of these local operators. Moreover
using a similar approach, we also get the weighted boundedness for the local
fractional maximal operators with rough kernel and local fractional integral
operators with rough kernel on Gaussian measure spaces.
