广义Morrey-Banach空间上双线性分数次积分算子及其交换子的估计  

Estimate for bilinear fractional integral operator and its commutator on generalized Morrey-Banach spaces

作　　者：李雪梅 逯光辉 LI Xue-mei;LU Guang-hui(College of Mathematics and Statistics,Northwest Normal University,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）》2024年第4期473-484,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12201500);甘肃省青年科技基金计划(22JR5RA173);西北师范大学2022年度研究生科研资助项目(2022KYZZ-S121)。

摘　　要：该文讨论了双线性分数次积分算子B_(α)及其交换子B_(α,b1,b2)在广义MorreyBanach空间M_(u)(X)上的有界性.在假设Lebesgue可测函数u满足某些特定的条件下,证明了B_(α)是从乘积空间M_(u1)(X_(1))×M_(u2)(X_(2))到空间M_u(Y)有界的.进一步,证明了由b_(1),b_(2)∈BMO(X)和B_α生成的交换子B_(α,b1,b2)是从乘积空间M_(u1)(X_(1))×M_(u2)(X_(2))到空间M_(u)(Y)有界的,其中u_(1)u_(2)=u.In this paper,the authors mainly discuss the boundedness of bilinear fractional inte-gral operator Bα and its commutator Bα,b1,b2 on generalized Morrey-Banach spaces Mu(X).Under assumption that the Lebesgue measurable function u satisfies some certain conditions,the anthors prove bilinear fractional integral operator Bαis bounded from product spaces Mu_(1)(X_(1))×Mu_(2)(X_(2))into spaces Mu(Y).Further,the paper also proves that the commutator Bα,b_(1),b_(2) generated by b_(1),b_(2)∈BMO(X)and Bαare bounded from product spaces Mu_(1)(X_(1))×Mu_(2)(X_(2))into spaces Mu(Y),where u_(1)u_(2)=u.

关 键 词：广义Morrey-Banach空间 双线性分数次积分算子 交换子 BMO(R^(n))空间 有界性 

分 类 号：O174.2[理学—数学]