Riesz potential and its commutators on Orlicz spaces

In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator Iα on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1):247-286, 2011) found necessary and sufficient conditions on general Young functions Φ and Ψ ensuring that this operator is of weak or strong type from LΦ into LΨ. Our characterizations for the boundedness of the above-mentioned operator are different from the ones in (Cianchi in J. Lond. Math. Soc. 60(1):247-286, 2011). As an application of these results, we consider the boundedness of the commutators of Riesz potential operator [ b, Iα] on Orlicz spaces when b belongs to the BMO and Lipschitz spaces, respectively. © 2017, The Author(s).

Авторы
Guliyev V.S. 1, 2 , Deringoz F.1 , Hasanov S.G.3
Редакторы
-
Издательство
Springer International Publishing
Номер выпуска
1
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
75
Том
2017
Год
2017
Организации
  • 1 Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
  • 2 S.M. Nikol’skii Institute of Mathematics, RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
  • 3 Ganja State University, Ganja, Azerbaijan
Ключевые слова
BMO; commutator; Lipschitz space; Orlicz space; Riesz potential
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5142/