Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces  

作　　者：Bo Ning DI Qian Jun HE Dun Yan YAN 

机构地区：[1]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,P.R.China [2]School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第7期1203-1228,共26页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11871452 and 12071473);Beijing Information Science and Technology University Foundation(Grant Nos.2025031)。

摘　　要：In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.

关 键 词：Local fractional integral local fractional maximal operator two-weight inequality Gaussian measure space 

分 类 号：O178[理学—数学]