论文标题
加权不平等，涉及两个耐心的整体操作员的迭代
Weighted inequalities involving iteration of two Hardy integral operators
论文作者
论文摘要
令$ 1 \ leq p <\ infty $和$ 0 <q，r <\ infty $。我们表征了不平等的有效性，\ begin {equination*} \ bigG（\ int_a^b \ bigG（\ int_a^x \ bigG（\ int_a^t f（int_a^t f（s） \ bigG）^{\ frac {1} {r}} \ leq c \ big（\ int_a^b f^p（x） a <b \ leq \ infty $。我们构建了一种比文献中先前提出的更直接的离散方法，我们以离散和连续形式的不平等来表征这种不平等。
Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize validity of the inequality for the composition of the Hardy operator, \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*} for all non-negative measurable functions on $(a,b)$, $-\infty \leq a < b \leq \infty$. We construct a more straightforward discretization method than those previously presented in the literature, and we characterize this inequality in both discrete and continuous forms.
