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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GÜRBÜZ F.

International Journal of Nonlinear Sciences and Numerical Simulation, vol.21, pp.715-726, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 21
  • Publication Date: 2020
  • Doi Number: 10.1515/ijnsns-2019-0111
  • Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.715-726
  • Keywords: Aαp,q weight, Multi-sublinear fractional maximal operator, Multilinear fractional integral operator, Rough kernel
  • Hakkari University Affiliated: Yes

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(Rn) 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.