Abstract The aim of this paper is to get the product L p ${L}^{p}$ -estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author also studies two-weighted weak type estimate on product L p ( ℝ n ) ${L}^{p}\left({\mathrm{\mathbb{R}}}^{n}\right)$ for rough multi-sublinear fractional maximal operators. In fact, this article is the rough kernel versions of [C. E. Kenig and E. M. Stein, “Multilinear estimates and fractional integration,” Math. Res. Lett., vol. 6, pp. 1–15, 1999, Y. Shi and X. X. Tao, “Weighted L p ${L}_{p}$ boundedness for multilinear fractional integral on product spaces,” Anal. Theory Appl., vol. 24, no. 3, pp. 280–291, 2008]'s results.

中文翻译：

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关于粗多线性分数积分和多次线性分数极大算子在乘积 Lp 和加权 Lp 空间上的行为

摘要 本文的目的是分别得到粗多线性分数积分算子和粗多次线性分数极大算子的乘积L p ${L}^{p}$ -估计、加权估计和二加权估计。作者还研究了乘积 L p ( ℝ n ) ${L}^{p}\left({\mathrm{\mathbb{R}}}^{n}\right)$多次线性分数极大值算子。事实上，这篇文章是 [CE Kenig 和 EM Stein，“Multilinear估计和分数积分，”Math. 水库 莱特，卷。6，第 1-15 页，1999 年，Y. Shi 和 XX Tao，“乘积空间上多线性分数积分的加权 L p ${L}_{p}$ 有界性”，Anal。理论应用，卷。24，没有。3, pp. 280–291, 2008] 的结果。