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作者机构：School of Mathematics Science Heilongjiang University Haerbin 150080 China School of Mathematics Beijing Normal University Beijing 100875 China School of Mathematics Graduate University Chinese Academy of Sciences Beijing 100049 China
出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)
年 卷 期：2012年第55卷第12期
页 面：2469-2480页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by National Natural Science Foundation of China (Grant Nos.11071250 and 10931001)
主 题：n-dimensional Hardy operator Hausdorff-Young inequality power weight
摘 要：In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)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 Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 p = q +∞, norms of the operators H and H* are obtained.
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