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.

Авторы
Guliyev V. 1, 2, 3 , Mammadov Y.4, 5 , Muslumova F.5
Редакторы
-
Издательство
Birkhauser Verlag AG
Номер выпуска
4
Язык
Английский
Страницы
1699-1717
Статус
Опубликовано
Подразделение
-
Номер
-
Том
11
Год
2020
Организации
  • 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
Ключевые слова
BMO; Commutator; Dunkl operator; Fractional maximal operator; Orlicz space
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/64307/