双线性分数次极大算子的交换子在Multi-Morrey空间上的紧性

The Compactness of Commutators of Bilinear Fractional Maximal Operators on Multi-Morrey Spaces

定义Mα为双线性分数次极大算子以及令b→=(b 1,b 2)是一个局部可积函数集合,得到双线性分数次极大算子与CMO(C∞c在BMO范数下的闭包)函数生成的交换子是Morrey空间到Multi-Morrey空间的紧算子,其中交换子包括分数次极大线性交换子Mα,b→和分数次极大迭代交换子Mα,Πb→,且得到的结论在单线性时也是新的结果.

Denote be the bilinear fractional maximal operators by Mαand let b→=(b 1,b 2)be a collection of locally integrable functions.In this paper,we obtain that the commutators generated by the bilinear fractional maximal operators and the CMO(C∞c closure under the BMO norm)functions are compact operators from the Morrey spaces to the Multi-Morrey spaces,where the commutators include the fractional maximal linear commutators Mα,∑b→and fractional maximal iterator commutators Mα,∏b→.The conclusion of this paper is also new when the operators are linear.