Complex interpolation of the predual of Morrey spaces over measure spaces

We prove that block spaces defined on Rn with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.

Authors
Burenkov V.I. 3, 4 , Hakim D.I.1, 2 , Nakai E.5 , Sawano Y. 1 , Sobukawa T.6 , Tararykova T.V. 3, 4
Journal
Georgian Mathematical Journal
Publisher
De Gruyter
Language
English
Status
Published
Link
External link
DOI
10.1515/gmj-2019-2070
Year
2019
Organizations
  • 1 Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo, 192-0397, Japan
  • 2 Department of Mathematics, Bandung Institute of Technology, Jalan Ganesha 10, Bandung, 40132, Indonesia
  • 3 S. M. nikol'Skii Mathematical Institute, Peoples Friendship University of Russia, RUDN University, 6 Miklukho Maklay Str., Moscow, 117198, Russian Federation
  • 4 School of Mathematics, Cardiff University, Cardiff, CF24 4AG, United Kingdom
  • 5 Department of Mathematics, Ibaraki University, Mito, Ibaraki, 310-8512, Japan
  • 6 Global Education Center, Waseda University, Nishi-Waseda 1-6-1, Shinjuku-ku, Tokyo, 1698050, Japan
Keywords
block spaces; complex interpolation method; Morrey spaces; preduals of Morrey spaces
Date of creation
24.12.2019
Date of change
21.07.2021
Short link
https://repository.rudn.ru/en/records/article/record/55544/
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