涉及两个 Hardy 积分算子迭代的加权不等式
泛函分析
2023-01-24 v3
摘要
设 且 。我们刻画了 Hardy 算子复合的不等式的有效性，\begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt \bigg)^{\frac{r}{q}} w(x) dx \bigg)^{\frac{1}{r}} \leq C \bigg(\int_a^b f^p(x) v(x) dx \bigg)^{\frac{1}{p}} \end{equation*} 对 上所有非负可测函数成立，。我们构造了比文献中先前提出的更为直接的离散化方法，并以离散与连续两种形式刻画了该不等式。
引用
@article{arxiv.2201.11437,
title = {Weighted inequalities involving iteration of two Hardy integral operators},
author = {Amiran Gogatishvili and Tuğçe Ünver},
journal= {arXiv preprint arXiv:2201.11437},
year = {2023}
}