Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

GÜRBÜZ F., Ding S., Han H., Long P.

International Journal of Nonlinear Sciences and Numerical Simulation, vol.22, no.6, pp.721-739, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1515/ijnsns-2019-0180
  • 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.721-739
  • Keywords: commutator, rough kernel, singular integral operator, variable exponent, variable exponent vanishing generalized Morrey space
  • Hakkari University Affiliated: Yes

Abstract

In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón-Zygmund type singular integral operator, rough Hardy-Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.