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The aim of this paper is to get the productL  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 productL  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, “WeightedL  p${L}_{p}$boundedness for multilinear fractional integral on product spaces,”  Anal. Theory Appl. , vol. 24, no. 3, pp. 280–291, 2008]'s results.

international journal of nonlinear sciences and numerical simulation

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