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

  • Nəşrin Növü: Article / Article
  • Cild: 174 Say: 3
  • Nəşr tarixi: 2020
  • jurnalın adı: Transactions of A. Razmadze Mathematical Institute
  • Jurnalın baxıldığı indekslər: Emerging Sources Citation Index (ESCI), Scopus
  • Səhifə sayı: pp.325-341
  • Açar sözlər: Commutator, G − BMO space, G-Fractional integral, G-Fractional maximal operator
  • Adres: Bəli

Qısa məlumat

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.