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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equivalent quasi-norms on Lorentz spaces


Authors: David E. Edmunds and Bohumír Opic
Journal: Proc. Amer. Math. Soc. 131 (2003), 745-754
MSC (2000): Primary 46E30, 26D10, 47B38, 47G10
Published electronically: October 15, 2002
MathSciNet review: 1937412
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Abstract: We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.


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Additional Information

David E. Edmunds
Affiliation: Centre for Mathematical Analysis and Its Applications, University of Sussex, Falmer, Brighton BN1 9QH, England
Email: d.e.edmunds@sussex.ac.uk

Bohumír Opic
Affiliation: Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
Email: opic@math.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06870-3
PII: S 0002-9939(02)06870-3
Keywords: Lorentz spaces, equivalent quasi-norms, weighted norm inequalities, fractional maximal operators, Riesz potentials, Hilbert transform
Received by editor(s): July 1, 2001
Published electronically: October 15, 2002
Additional Notes: This research was supported by NATO Collaborative Research Grant PST.CLG 970071 and by grant no.201/01/0333 of the Grant Agency of the Czech Republic
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society