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K-ENVELOPES FOR REAL INTERPOLATION METHODS

Published online by Cambridge University Press:  02 August 2012

MING FAN
Affiliation:
School of Technology and Business Studies, Dalarna University, 781 88 Borlänge, Sweden e-mail: fmi@du.se
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Abstract

In this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the KΦ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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