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

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.