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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $\alpha \in (0,1)$.
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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