Some Weighted Estimates on Gaussian Measure Spaces

TL;DR

This paper establishes weighted boundedness results for various local multilinear operators and fractional integrals on Gaussian measure spaces, introducing new radial definitions to facilitate analysis.

Contribution

It introduces novel radial definitions for local operators and proves their weighted boundedness on Gaussian measure spaces, extending previous results to rough kernels.

Findings

Weighted boundedness of local multilinear Hardy-Littlewood maximal operators

Weighted boundedness of local multilinear fractional integral operators with rough kernels

New radial definitions simplify the analysis of local operators

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.