Equivalent quasi-norms on Lorentz spaces

Edmunds, David; Opic, Bohumír

doi:10.1090/S0002-9939-02-06870-3

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
DOI: https://doi.org/10.1090/S0002-9939-02-06870-3
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: https://doi.org/10.1090/S0002-9939-02-06870-3
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