In the open range $1<p<q<\infty$, under a certain geometrical condition on weights, two-weight norm inequality for the product fractional integral operator, whose kernel has singularity appeared on each of the coordinate subspaces, is shown to follow from the Fefferman–Phong-type characteristic for the product cubes. This geometrical condition turns out to be the testing condition of Carleson-type embedding for product dyadic cubes.

中文翻译：

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乘积分数积分算子的二重范数不等式

在开放范围内 $\mathrm{1个}<p<q<\infty$在权重的特定几何条件下，乘积立方的Fefferman-Phong型特征可证明乘积分数积分算子的两重范数不等式（其核在每个坐标子空间上都出现了奇异性）。证明该几何条件是产品二元立方体的Carleson型嵌入的测试条件。