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The K-functional of certain pairs of rearrangement invariant spaces

Published online by Cambridge University Press:  17 April 2009

Jonathan Arazy
Jonathan Arazy
Affiliation:
Department of Mathematics, University of Haifa, Haifa, Israel.
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Abstract

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Let X, Y be rearrangement invariant spaces and let M = M(Y, X) be the space of all multipliers of Y into X. It is shown that if X = YM and some technical conditions are satisfied, then the K-functional K(t, f, X, Y) is equivalent to the expression

where ψ is the inverse of the fundamental function ϕM of M, defined by

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 2 , April 1983 , pp. 249 - 257
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Bergh, Jöran, Löfström, Jörgen, Interpolation spaces. An introduction (Die Grundlehren der mathematischen Wissenschaften, 223. Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[2]Holmstedt, Tord, “Interpolation of quasi-normed spaces”, Math. Scand. 26 (1970), 177–199.CrossRefGoogle Scholar
[3]Lindenstrauss, Joram, Tzafriri, Lior, Classical Banach spaces II. Function spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete, 97. Springer-Verlag, Berlin, Heidelberg, New York, 1979).Google Scholar
[4]Milman, Mario, “Interpolation of operators of mixed weak-strong type between rearrangement invariant spaces”, Indiana Univ. Math. J. 28 (1979), 985–992.CrossRefGoogle Scholar
[5]Milman, Mario, “The computation of the K-functional for couples of rearrangement invariant spaces”, submitted.Google Scholar
[6]Torchinsky, Alberto, “The K-functional for rearrangement invariant spaces”, Studia Math. 64 (1979), 175–190.CrossRefGoogle Scholar
[7]Zippin, M., “Interpolation of operators of weak type between rearrangement invariant function spaces”, J. Funct. Anal. 7 (1971), 267–284.CrossRefGoogle Scholar