Some Weighted Estimates on Gaussian Measure Spaces

Abstract

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.