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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Interpolation spaces between the Lipschitz class
and the space of continuous functions


Authors: Michael Cwikel and Mieczyslaw Mastylo
Journal: Proc. Amer. Math. Soc. 124 (1996), 1103-1109
MSC (1991): Primary 46M35, 46E15, 46E35
MathSciNet review: 1307507
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Abstract: It is shown that the complex interpolation spaces $[C([0,1]), \linebreak Lip_{1}([0,1])]_{\theta }$ 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 $\alpha \in (0,1)$.


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Additional Information

Michael Cwikel
Affiliation: Department of Mathematics, Technion Israel Institute of Technology, Haifa, 32000 Israel
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
Email: mastylo@math.amu.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03171-1
PII: S 0002-9939(96)03171-1
Keywords: Lipschitz class, complex interpolation space, Calder\'{o}n couple
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
Article copyright: © Copyright 1996 American Mathematical Society