On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product L p and weighted L p spaces

Abstract

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.