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.

Authors
Burenkov V.I. 1, 2 , Chigambayeva D.K.3 , Nursultanov E.D.4, 5
Journal
Complex Variables and Elliptic Equations
Number of issue
1
Language
English
Pages
87-108
Status
Published
DOI
10.1080/17476933.2019.1664488
Volume
65
Year
2020
Organizations
  • 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
Keywords
Morrey spaces; Morrey-type spaces; Marcinkiewicz-type interpolation theorem; O'Neil-type inequality for convolutions; Riesz potential; singular integral operators
Date of creation
24.12.2019
Date of change
21.07.2021
Short link
https://repository.rudn.ru/en/records/article/record/55659/
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