We find a necessary and sufficient condition for the boundedness of an m-linear integral-type operator between weighted-type spaces of functions, and calculate norm of the operator, complementing some results by L. Grafakos and his collaborators. We also present an inequality which explains a detail in the proof of the boundedness of the linear integral-type operator on \(L^{p}({\mathbb {R}}^{n})\) space.

中文翻译：

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关于加权型空间之间的m线性积分型算子的范数的注记

我们为函数的加权型空间之间的m线性积分型算子的有界性找到了一个充要条件，并计算了该算子的范数，对L. Grafakos及其合作者的一些结果进行了补充。我们还提出了一个不等式，该不等式在\（L ^ {p}（{\ mathbb {R}} ^ {n}）\）空间上的线性积分型算子的有界性证明中作了详细解释。