度量测度空间上双线性θ-型Marcinkiewicz积分交换子  

Commutator of bilinearθ-type Marcinkiewicz integral on metric measure spaces

作　　者：逯光辉 LU Guang-hui(College of Math.Stat.,Northwest Normal Univ.,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《高校应用数学学报（A辑）》2020年第3期323-342,共20页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11561062);甘肃省高等学校创新基金(2020A-010);西北师范大学青年教师科研能力提升计划(NWNU-LKQN2020-07);西北师范大学博士启动金(6014/0002020203)。

摘　　要：设(X,d,μ)是Hytonen意义下满足几何双倍和上双倍条件的非齐型度量测度空间.在假设控制函数λ满足一定的ε-弱的逆双倍条件下,该文证明了由双线性θ-型Marcinkiewicz积分Mθ与具离散系数的正则有界平均振荡空间RBMO(μ)生成的交换子Mθ,b1,b2从L^p1(μ)×L^p2(μ)到L^p(μ)是有界的,其中1<p1,p2<∞且满足1/p=1/p1+1/p2.进一步,还得到了交换子Mθ,b1,b2在Morrey空间上的有界性.Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling and upper doubling conditions in the sense of Hyt?onen.Under the assumption that the dominating functionλsatisfies the-weak reverse doubling condition,the author proves that the commutator Mθ,b1,b2 generated by the bilinearθ-type Marcinkiewicz integral Mθand the space bε-RBMO(μ)with discrete coefficient is bounded from L^p1(μ)×L^p2(μ)into L^p(μ),where 1/p=1/p1+1/p2 with 1<p1,p2<∞.Furthermore,the boundedness of the Mθ,b1,b2 on Morrey space is also obtained.

关 键 词：非齐型度量测度空间 交换子 双线性θ-型Marcinkiewicz积分 RBMO(μ)空间 MORREY空间 

分 类 号：O174.2[理学—数学]