Let be a ball Banach function space on . We introduce the class of weights . Assuming that the Hardy-Littlewood maximal function is bounded on and , we obtain that . As a consequence, we have , where is the variable exponent Lebesgue space. As an application, if a linear operator is bounded on the weighted ball Banach function space for any , then the commutator is bounded on with .

中文翻译：

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球Banach函数空间上的权重生成的BMO函数

设球为Banach函数空间。我们介绍权重的类别。假设Hardy-Littlewood最大值函数在和上有界，我们得到。结果，我们有，其中变量指数Lebesgue空间在哪里。作为应用，如果一个线性算子为界对加权球的Banach函数空间对于任何，然后换向器必然与。