Boundedness of higher order commutators of g-fractional integral and g-fractional maximal operators with G − BMO functions

Ibrahimov E. J., Dadashova G. A., Jafarova S. A.

Transactions of A. Razmadze Mathematical Institute, vol.174, no.3, pp.325-341, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 174 Issue: 3
  • Publication Date: 2020
  • Journal Name: Transactions of A. Razmadze Mathematical Institute
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.325-341
  • Keywords: Commutator, G − BMO space, G-Fractional integral, G-Fractional maximal operator
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In this paper we introduce the Gegenbauer BMO (G − BMO) space and study its basic properties, analogous to the classical case. The John-Nirenberg type theorem is proved for f ∈ BMOG(R+). Moreover, the notions of a higher order commutator of Gegenbauer fractional (G-fractional) integral JGb,α,k and Gegenbauer fractional (G-fractional) maximal operator MGb,α,k with G− BMO function are studied. When commutator b is a (G− BMO) function, the necessary and sufficient conditions for (Lp; Lq) boundedness of commutators JGb,α,k and MGb,α,k are obtained.