分数次Orlicz极大算子在齐型空间中的局部加权端点估计

Weighted endpoint estimates for the Orlicz fractional maximal operator on a bounded domain of homogeneous spaces

利用齐型空间中的覆盖引理及其有界区域的二进方体分解得到了分数次Orlicz极大算子在齐型空间(X,d,μ)中的有界区域上的局部加权端点估计.该工作为分数次积分交换子[b,Iα]在欧式空间Rn中的有界区域上的加权端点弱型估计推广到齐型空间奠定了基础.

In this paper, we obtained the weighted endpoint estimates of the Orlicz fractional maximal operator by use of the covering lemma and the dyadic cube decomposition of the bounded domain in the homogeneous spaces. These results lay foundation for us to extend the weighted endpoint estimates for the commutator of fractional integral operator on the bounded domain in Rn to the homogeneous spaces.