Interpolation spaces between the Lipschitz class and the space of continuous functions
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- by Michael Cwikel and Mieczyslaw Mastylo PDF
- Proc. Amer. Math. Soc. 124 (1996), 1103-1109 Request permission
Abstract:
It is shown that the complex interpolation spaces $[C([0,1]), Lip_{1}([0,1])]_{\theta }$ and $[C([0,1]),Lip_{1}([0,1])]^{\theta }$ do not coincide with $Lip_{ \theta }([0,1])$ or $lip_{\theta }([0,1])$ and also that the couple $(C,Lip_{1})$ is not a Calderón couple. Similar results are also obtained for the couples $(C,Lip_{\alpha })$ and $(Lip_{\alpha },Lip_{1})$ when $\alpha \in (0,1)$.References
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Additional Information
- Michael Cwikel
- Affiliation: Department of Mathematics, Technion Israel Institute of Technology, Haifa, 32000 Israel
- MR Author ID: 53595
- Email: mcwikel@techunix.technion.ac.il
- Mieczyslaw Mastylo
- Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
- MR Author ID: 121145
- Email: mastylo@math.amu.edu.pl
- Received by editor(s): September 2, 1994
- Additional Notes: The research of the first author was supported by the Fund for Promotion of Research at the Technion. The research of the second author was supported in part by a Lady Davis Fellowship at the Technion.
- Communicated by: Dale Alspach
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1103-1109
- MSC (1991): Primary 46M35, 46E15, 46E35
- DOI: https://doi.org/10.1090/S0002-9939-96-03171-1
- MathSciNet review: 1307507