Morrey-type estimates for commutator of fractional integral associated with Schrödinger operators on the Heisenberg group

Let L=−ΔHn+V be a Schrödinger operator on the Heisenberg group Hn, where the nonnegative potential V belongs to the reverse Hölder class RHq1 for some q1≥ Q/ 2 , and Q is the homogeneous dimension of Hn. Let b belong to a new Campanato space Λνθ(ρ), and let IβL be the fractional integral operator associated with L. In this paper, we study the boundedness of the commutators [b,IβL] with b∈Λνθ(ρ) on central generalized Morrey spaces LMp,φα,V(Hn), generalized Morrey spaces Mp,φα,V(Hn), and vanishing generalized Morrey spaces VMp,φα,V(Hn) associated with Schrödinger operator, respectively. When b belongs to Λνθ(ρ) with θ> 0 , 0 < ν< 1 and (φ1, φ2) satisfies some conditions, we show that the commutator operator [b,IβL] is bounded from LMp,φ1α,V(Hn) to LMq,φ2α,V(Hn), from Mp,φ1α,V(Hn) to Mq,φ2α,V(Hn), and from VMp,φ1α,V(Hn) to VMq,φ2α,V(Hn), 1 / p− 1 / q= (β+ ν) / Q. © 2018, The Author(s).

Authors
Guliyev V.S. 1, 2, 3 , Akbulut A.1 , Namazov F.M.4
Publisher
Springer International Publishing
Number of issue
1
Language
English
Status
Published
Number
273
Volume
2018
Year
2018
Organizations
  • 1 Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
  • 2 Institute of Mathematics and Mechanics, NAS of Azerbaijan, Baku, Azerbaijan
  • 3 S.M. Nikolskii Institute of Mathematics, RUDN University, Moscow, Russian Federation
  • 4 Baku State University, Baku, Azerbaijan
Keywords
BMO; Campanato space; Central generalized Morrey space; Commutator; Fractional integral; Heisenberg group; Schrödinger operator
Date of creation
04.02.2019
Date of change
04.02.2019
Short link
https://repository.rudn.ru/en/records/article/record/36217/
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