Hausdorff算子的双权范数估计  

Two-Weight Norm Estimates for Hausdorff Operators

作　　者：杨帅 李宝德[1] YANG Shuai;LI Baode(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第4期398-404,共7页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Function spaces adapted to multi-level anisotropic ellipsoid covers and the boundedness of related operators”(2020D01C048);the National Natural Science Foundation of the People’s Republic of China“Real-variable theory of variable exponential functions on anisotropic Euclidean spaces and its applications”(12261083).

摘　　要：Hausdorff算子的核函数在满足一定条件时,其在加权Lebesgue空间上的双权不等式已经被建立.研究了定义在R+上的Hausdorff算子,当Hausdorff算子的核函数在更弱的条件下仍能建立相应的双权不等式,并给出了满足这种条件的具体核函数的例子.Two-weight inequalities for Hausdorff operators have been established in weighted Lebesgue spaces under certain assumptions of kernel function.We study the Hausdorff operators of special kind on the real line R+and also establish corre-sponding two-weight inequalities under weaker assumptions of kernel function.Then we give some specific examples that satisfy these conditions of kernel function.

关 键 词：Hausdorff算子 加权Lebesgue空间 权函数 

分 类 号：O177.6[理学—数学]