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ISSN 1088-6826(e) ISSN 0002-9939(p)

Are generalized Lorentz ``spaces'' really spaces?

Author(s): Michael Cwikel; Anna Kaminska; Lech Maligranda; Lubos Pick
Journal: Proc. Amer. Math. Soc. 132 (2004), 3615-3625.
MSC (2000): Primary 46E30, 46B42
Posted: 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 . We establish necessary and sufficient conditions on and 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
Email: mcwikel@math.technion.ac.il

Anna Kaminska
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Email: kaminska@memphis.edu

Lech Maligranda
Affiliation: Department of Mathematics, Lulea University of Technology, SE-971 87 Lulea, Sweden
Email: lech@sm.luth.se

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
Email: pick@karlin.mff.cuni.cz

DOI: 10.1090/S0002-9939-04-07477-5
PII: S 0002-9939(04)07477-5
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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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