加权Hardy-Littlewood 平均算子的交换子在Herz型空间上的有界性
The Boundedness of Commutator Associated to Weighted Hardy-Littlewood Average Operator in Herz-type Spaces
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摘要: 主要讨论了加权Hardy-Littlewood 平均算子U_\psi与BMO函数b生成的交换子在Herz型空间和Morrey型 Herz空间上的有界性，并给出了其在Morrey型 Herz空间上有界的充分条件是 \int_0^1t^-(\alpha+n/q_2-\lambda)\psi(t)\log\frac2tdt\infty. 若\alpha=0，\lambda=0，q_1=q_2=p1，则\int_0^1t^-(\alpha+n/q_2-\lambda)\psi(t)\log\frac2tdt=\int_0^1t^-n/p\psi(t)\log\frac2tdt\infty， 此时交换子U_\psi^b是L^p(R^n)空间上的有界算子.Abstract: The boundedness of commutator U_\psi^b generated by the Weighted Hardy-Littlewood average operator U_\phi and BMO function b in Herz and Morrey-Herz type spaces are discussed. It is showed that the sufficient condition for its boundedness in the Morrey-Herz type spaces is \int_0^1t^-(\alpha+n/q_2-\lambda)\psi(t)\log\frac2tdt\infty. It turned to be \int_0^1t^-n/p\psi(t)\log\frac2tdt\infty as \alpha=0, \lambda=0 and q_1=q_2=p1, and then U_\psi^b is bounded on L^p(R^n).
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