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

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Abstract

The aim of this paper is to get the product Lp-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 Lp(n) 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 Lp boundedness for multilinear fractional integral on product spaces,” Anal. Theory Appl., vol. 24, no. 3, pp. 280–291, 2008]'s results.


Corresponding author: Ferit Gürbüz, Department of Mathematics Education, Faculty of Education, Hakkari University, Hakkari, Turkey, E-mail:

  1. Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.

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Received: 2019-04-12
Accepted: 2020-05-26
Published Online: 2020-08-12
Published in Print: 2020-11-18

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