Explicit constants for Hardy's inequality with power weight on n-dimensional product spaces
Explicit constants for Hardy's inequality with power weight on n-dimensional product spaces
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n 维乘积空间上具有幂权重的 Hardy 不等式的显式常数
DOI：
10.1007/s11425-012-4453-4
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发表时间：
2012-12-01
影响因子：
1.4
通讯作者：
Yan DunYan
中科院分区：
文献类型：
--
作者：
Wang ShiMo;Lu ShanZhen;Yan DunYan
本文研究了n维乘积空间G=(0，无穷)(N)上的Hardy算子H及其伴随算子H*。我们使用新的方法得到两个主要结果。一是刻画了算子H和H*从L(P)(G，x(α))到L(Q)(G，x(β))有界的充要条件，并明确地给出了算子H和H*的界。二是当1<；p=q<；+无穷大时，得到了算子H和H*的范数。
In this paper, Hardy operator H on n-dimensional product spaces G = (0,infinity) (n) and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from L (p) (G, x (alpha)) to L (q) (G, x (beta) ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < + infinity, norms of the operators H and H* are obtained.