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