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

DOI:
https://doi.org/10.1090/S0002-9939-96-03171-1

MathSciNet review:
1307507

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the complex interpolation spaces and do not coincide with or and also that the couple is not a Calderón couple. Similar results are also obtained for the couples and when .

**1.**J. Bergh,*On the relation between the two complex methods of interpolation*, Indiana Univ. Math. J.**28**(1979), 775--778. MR**80f:46062****2.**J. Bergh and J. Löfström,*Interpolation spaces. An introduction*, Grundlehren Math. Wiss., vol. 223, Springer, Berlin, Heidelberg, and New York, 1976. MR**58:2349****3.**Y. Brudnyi and N. Krugljak,*Interpolation functors and interpolation spaces*, North-Holland, Amsterdam, New York, Oxford, and Tokyo, 1991. MR**93b:46141****4.**Y. Brudnyi and A. Shteinberg,*Calderón couples of Lipschitz spaces*, J. Functional Analysis**131**(1995), 459--498. CMP**95:16****5.**------,*Calderón constants of finite dimensional couples*, Israel J. Math. (to appear).**6.**T. Bychkova,*Couples without C-properties*, Investigations in the Theory of Functions of Several Variables, Yaroslavl, 1990, pp. 18--51.**7.**A. P. Calderón,*Intermediate spaces and interpolation, the complex method*, Studia Math.**24**(1964), 113--190. MR**29:5097****8.**M. Cwikel,*Complex interpolation, a discrete definition and reiteration*, Indiana Univ. Math. J.**27**(1978), 1005--1009. MR**80h:46118****9.**------,*Monotonicity properties of interpolation spaces*II, Ark. Mat.**19**(1981), 123--136. MR**83a:46082****10.**------,*-divisibility of the -functional and Calderón couples*, Ark. Mat.**22**(1984), 39--62. MR**85m:46074****11.**M. Cwikel and Y. Sagher,*Relations between real and complex interpolation spaces*, Indiana Univ. Math. J.**36**(1987), 905--912. MR**88m:46083****12.**T. Holmstedt,*Interpolation of quasi-normed spaces*, Math. Scand.**26**(1970), 177--199. MR**54:3440****13.**V. I. Ovchinnikov,*Interpolation properties of fractional BMO space*, Abstracts of Proceedings of the 13th All-Union School in Operator Theory in Functional Spaces, Kuibyshev, 1988.**14.**J. Peetre,*Exact interpolation theorems for Lipschitz continuous functions*, Richerche Mat.**18**(1969), 239--259. MR**42:841**

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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:
https://doi.org/10.1090/S0002-9939-96-03171-1

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