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Are generalized Lorentz ``spaces'' really spaces?

Authors: Michael Cwikel, Anna Kaminska, Lech Maligranda and Lubos Pick
Journal: Proc. Amer. Math. Soc. 132 (2004), 3615-3625
MSC (2000): Primary 46E30, 46B42
Published electronically: July 20, 2004
MathSciNet review: 2084084
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Abstract: We show that the Lorentz space $\Lambda^p(w)$need not be a linear set for certain ``non-classical" weights $w$. We establish necessary and sufficient conditions on $p$ and $w$ for this situation to occur.

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Additional Information

Michael Cwikel
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Anna Kaminska
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152

Lech Maligranda
Affiliation: Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Lubos Pick
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic – and – Department of Mathematics, Brock University, 500 Glenridge Ave., St. Catharines, Ontario, Canada L2S 3A1

Keywords: Lorentz spaces, Marcinkiewicz spaces, Lorentz-Orlicz spaces, weights, rearrangement
Received by editor(s): January 21, 2003
Received by editor(s) in revised form: July 16, 2003
Published electronically: July 20, 2004
Additional Notes: The first named author was supported by the Dent Charitable Trust—Non-Military Research Fund and by the Fund for Promotion of Research at the Technion. The second named author was supported by project no. SMK–2136 of the Kempe Foundation in Sweden. The third named author was supported by the Swedish Natural Science Research Council (NFR)–grant M5105-20005228/2000. The fourth named author was supported by grant no. 201/01/0333 of the Grant Agency of the Czech Republic and by grant no. MSM 113200007 of the Czech Ministry of Education.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society