Characterization of fractional maximal operator and its commutators on Orlicz spaces in the Dunkl setting

On the Rd the Dunkl operators {Dk,j}j=1d are the differential-difference operators associated with the reflection group Z2d on Rd. In this paper, in the setting Rd we find necessary and sufficient conditions for the boundedness of the fractional maximal operator Mα,k on Orlicz spaces LΦ,k(Rd). As an application of this result we show that b∈ BMOk(Rd) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ,k(Rd). © 2020, Springer Nature Switzerland AG.

Authors
Guliyev V. 1, 2, 3 , Mammadov Y.4, 5 , Muslumova F.5
Journal
Journal of Pseudo-Differential Operators and Applications
Publisher
Birkhauser Verlag AG
Number of issue
4
Language
English
Pages
1699-1717
Status
Published
Link
External link
DOI
10.1007/s11868-020-00364-w
Volume
11
Year
2020
Organizations
  • 1 Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan
  • 2 Department of Mathematics, Dumlupinar University, Kutahya, Turkey
  • 3 S.M. Nikolskii Institute of Mathematics at RUDN University, Moscow, Russian Federation
  • 4 Department of Informatics, Nakhchivan State University, Nakhchivan, Azerbaijan
  • 5 Nakhchivan Teacher-Training Institute, Nakhchivan, Azerbaijan
Keywords
BMO; Commutator; Dunkl operator; Fractional maximal operator; Orlicz space
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/64307/
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