Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries

We introduce a class of Morrey-type spaces , which includes the classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem for such spaces. This theorem is then applied to obtaining an analogue of O'Neil's inequality for convolutions and to proving the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operators.

Авторы
Burenkov V.I. 1, 2 , Chigambayeva D.K.3 , Nursultanov E.D.4, 5
Номер выпуска
1
Язык
Английский
Страницы
87-108
Статус
Опубликовано
Том
65
Год
2020
Организации
  • 1 RUDN Univ, SM Nikolskii Inst Math, Moscow, Russia
  • 2 Russian Acad Sci, VA Steklov Inst Math, Moscow, Russia
  • 3 LN Gumilyov Eurasian Natl Univ, Sch Mech & Math, Nur Sultan, Kazakhstan
  • 4 Moscow MV Lomonosov State Univ, Kazakhstan Branch, Dept Math, Nur Sultan, Kazakhstan
  • 5 Inst Math & Math Modeling, Alma Ata, Kazakhstan
Ключевые слова
Morrey spaces; Morrey-type spaces; Marcinkiewicz-type interpolation theorem; O'Neil-type inequality for convolutions; Riesz potential; singular integral operators
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55659/