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Complex interpolation of the predual of Morrey spaces over measure spaces

  • Victor I. Burenkov , Denny I. Hakim EMAIL logo , Eiichi Nakai , Yoshihiro Sawano , Takuya Sobukawa und Tamara V. Tararykova
Veröffentlicht/Copyright: 26. November 2019
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Abstract

We prove that block spaces defined on n 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.

MSC 2010: 42B35; 46B70; 46B26

Award Identifier / Grant number: 15H03621

Award Identifier / Grant number: 16K05209

Award Identifier / Grant number: 18-51-06005

Funding statement: V. I. Burenkov was supported by the “Peoples” Friendship University of Russia (RUDN University) Programme 5-100. E. Nakai and T. Sobukawa were supported by Grant-in-Aid for Scientific Research (B) (no. 15H03621), Japan Society for the Promotion of Science. Y. Sawano was supported by Grant-in-Aid for Scientific Research (C) (no. 16K05209), Japan Society for the Promotion of Science. T. V. Tararykova was supported by the Russian Foundation for Basic Research (no. 18-51-06005).

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Received: 2017-11-28
Accepted: 2018-10-18
Published Online: 2019-11-26
Published in Print: 2021-06-01

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