Complex interpolation of vanishing Morrey spaces

We describe the first and second complex interpolations of vanishing Morrey spaces, introduced in Almeida and Samko (J Funct Anal 2726:2392–2411, 2017 ) and Chiarenza and Franciosi (Ann Mat Pura Appl 161(4):285–297, 1992 ). In addition, we show that the diamond subspace in Hakim et al. (Constr Appro...

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Bibliographic Details
Published in:Annals of functional analysis 2020-07, Vol.11 (3), p.643-661
Main Authors: Hakim, Denny Ivanal, Sawano, Yoshihiro
Format: Article
Language:English
Subjects:
Functional Analysis
Mathematics
Mathematics and Statistics
Original Paper
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Summary:We describe the first and second complex interpolations of vanishing Morrey spaces, introduced in Almeida and Samko (J Funct Anal 2726:2392–2411, 2017 ) and Chiarenza and Franciosi (Ann Mat Pura Appl 161(4):285–297, 1992 ). In addition, we show that the diamond subspace in Hakim et al. (Constr Approx 46:489–563, 2017 ) and one of the function spaces in [ 1 ] are the same. We also give several examples for showing that each of the complex interpolations of these spaces is different.
ISSN:2639-7390
2008-8752
DOI:10.1007/s43034-019-00045-w