论文标题
在加权强壮的不等式上，二维矩形操作员 - E.锯耶定理的扩展
On weighted Hardy inequality with two-dimensional rectangular operator -- extension of the E. Sawyer theorem
论文作者
论文摘要
$ \ mathbb {r}^2 _+$在$ \ mathbb {r}^2 _+$上获得的那对重量$ v $和$ w $的表征是一个表征，为此，两维的矩形集成运算符是从加权的lebesgue space $ l^p_v（\ m}^r}^r}^2 _+l^Q_____的$ l^p_v（r} $ l^q_w（r^q q q） $ 1 <p \ not = q <\ infty $，这是E. Sawyer的结果\ Cite {Saw1}的必要补充，价格为$ 1 <p \ leq Q <\ infty $。此外，我们声明E. sawyer定理是实际的，如果$ p = q $，对于$ p <q $，标准不那么复杂。 $ q <p $是新的。
A characterization is obtained for those pairs of weights $v$ and $w$ on $\mathbb{R}^2_+$, for which the two--dimensional rectangular integration operator is bounded from a weighted Lebesgue space $L^p_v(\mathbb{R}^2_+)$ to $L^q_w(\mathbb{R}^2_+)$ for $1<p\not= q<\infty$, which is an essential complement to E. Sawyer's result \cite{Saw1} given for $1<p\leq q<\infty$. Besides, we declare that the E. Sawyer theorem is actual if $p=q$ only, for $p<q$ the criterion is less complicated. The case $q<p$ is new.
