关于高维乘积空间上\(p -\)adic 哈代型算子的精确估计。
Sharp estimates for the -adic Hardy type operators on higher-dimensional product spaces.
作者信息
Liu Ronghui, Zhou Jiang
机构信息
College of Mathematics and System Science, Xinjiang University, Urumqi, 830046 People's Republic of China.
出版信息
J Inequal Appl. 2017;2017(1):219. doi: 10.1186/s13660-017-1491-z. Epub 2017 Sep 12.
In this paper, we introduce the -adic Hardy type operator and obtain its sharp bound on the -adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the -adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted -adic Hardy type operator is bounded on the -adic Lebesgue product spaces. Furthermore, the -adic weighted Hardy-Cesàro operator is also obtained.
在本文中，我们引入了(p)-进Hardy型算子，并在(p)-进Lebesgue乘积空间上得到了其精确界。同时，对于带幂权的(p)-进Lebesgue乘积空间计算了一个类似的结果。此外，我们刻画了一个确保加权(p)-进Hardy型算子在(p)-进Lebesgue乘积空间上有界的充分必要条件。此外，还得到了(p)-进加权Hardy-Cesàro算子。
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