与一般正测度对应的哈代算子的尖锐常数
Sharp constant of Hardy operators corresponding to general positive measures.
作者信息
Nie Xudong, Yan Dunyan
机构信息
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, P.R. China.
2School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, P.R. China.
出版信息
J Inequal Appl. 2018;2018(1):78. doi: 10.1186/s13660-018-1660-8. Epub 2018 Apr 10.
We investigate a new kind of Hardy operator [Formula: see text] with respect to arbitrary positive measures and prove that [Formula: see text] is bounded on [Formula: see text] with an upper constant [Formula: see text]. Moreover, we characterize a sufficient condition about the measure which makes [Formula: see text] to be the [Formula: see text]-norm of [Formula: see text].
我们针对任意正测度研究一种新型的哈代算子[公式：见原文]，并证明[公式：见原文]在[公式：见原文]上有界，其上界常数为[公式：见原文]。此外，我们刻画了关于测度的一个充分条件，该条件使得[公式：见原文]成为[公式：见原文]的[公式：见原文]范数。
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