Local Muckenhoupt weights on Gaussian measure spaces

We study an analogue of ApAp weights which are called local weights and denoted by Ap,aAp,a in Gauss measure spaces. Some classical properties of it are obtained. Then we characterize the weights by the boundedness of local Hardy–Littlewood maximal operators on weighted Lebesgue spaces. We also get the Jones's decomposition of Ap,aAp,a, which is different from the type of Orobitg and Peréz [24]. At last, we consider the class weights of Ap,q,aAp,q,a and obtain the weighted boundedness of fractional maximal operator Mβ,aMβ,a.