发表机构
Australian National University（澳大利亚国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对$L^1$中正指数幂加权的Stein-Weiss不等式，确定了新的较弱必要条件，补充了De Nápoli与Picon此前关于抵消条件的研究，完善了该类不等式的充要条件体系。
AI 中文摘要
我们针对一类正指数幂加权的$L^1$ Stein-Weiss不等式，得到了输入函数所需的充要条件。De Nápoli与Picon此前的研究表明，某一抵消条件在$L^1$中是充要的，但该条件在正指数幂加权情形下是否仍为必要条件尚不明确。本文确定了正指数幂加权的较弱必要条件，其中部分条件已在作者此前的工作中被证明对正非整数指数幂加权是充分的。
英文摘要
We obtain the necessary and sufficient conditions on input functions for a family of positive exponent power weight $L^1$ Stein-Weiss inequalities. Earlier work by De Nápoli and Picon showed that a certain cocanceling condition was necessary and sufficient in $L^1$, but it was unknown if this condition remained necessary in the positive exponent power weight setting. This present article identifies weaker necessary conditions for positive exponent power weights, some of which were shown to be sufficient for positive, non-integer exponent power weights in the author's earlier work.
Comments12 pages, comments welcome
