Interpolation between and

Authors:
Sergei V. Astashkin and Lech Maligranda

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2929-2938

MSC (2000):
Primary 46E30, 46B42, 46B70

Published electronically:
May 21, 2004

MathSciNet review:
2063112

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index , then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .

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Additional Information

**Sergei V. Astashkin**

Affiliation:
Department of Mathematics, Samara State University, Akad. Pavlova 1, 443011 Samara, Russia

Email:
astashkn@ssu.samara.ru

**Lech Maligranda**

Affiliation:
Department of Mathematics, Lulelå University of Technology, se-971 87 Luleå, Sweden

Email:
lech@sm.luth.se

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07425-8

Keywords:
$L_{p}$-spaces,
Lorentz spaces,
rearrangement invariant spaces,
Boyd indices,
interpolation of operators,
operators of strong type,
operators of weak type,
$K$-functional,
Marcinkiewicz spaces

Received by editor(s):
October 9, 2002

Published electronically:
May 21, 2004

Additional Notes:
This research was supported by a grant from the Royal Swedish Academy of Sciences for cooperation between Sweden and the former Soviet Union (project 35156). The second author was also supported in part by the Swedish Natural Science Research Council (NFR)-grant M5105-20005228/2000.

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2004
American Mathematical Society