NECESSARY AND SUFFICIENT CONDITIONS FOR GENERALIZED HAUSDORFF OPERATORS AND COMMUTATORS
NECESSARY AND SUFFICIENT CONDITIONS FOR GENERALIZED HAUSDORFF OPERATORS AND COMMUTATORS
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广义Hausdorff算子和换向器的充要条件
DOI：
10.15352/afa/06-3-6
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发表时间：
2015-01-01
影响因子：
1
通讯作者：
Wu, Xiaomei
中科院分区：
文献类型：
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作者：
Wu, Xiaomei
本文引入了一类广义Hausdorff算子，并刻画了这类算子在Lebesgue空间和中心Morrey空间上的有界性.此外，我们还得到了这些空间上的算子范数。我们还得到了保证其交换子在Lebesgue空间和符号在中心BMO空间中的中心Morrey空间上有界的充分必要条件。作为应用，我们给出了Lebesgue空间和中心Morrey空间上加权哈代算子和加权塞萨罗算子的一个新的上界估计方法.
In this paper, we introduce a type of generalized Hausdorff operators and characterize the boundedness of these operators on Lebesgue spaces and central Morrey spaces. Moreover, we obtain the operator norms on these spaces. We also obtain sufficient and necessary conditions which ensure the boundedness of their commutators on Lebesgue spaces and central Morrey spaces with symbols in central BMO spaces. As applications, we give a new method to obtain sharp bounds for weighted Hardy operators and weighted Cesaro operators on Lebesgue spaces and central Morrey spaces.