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Equivalent quasi-norms on Lorentz spaces
Author(s):
David
E.
Edmunds;
Bohumír
Opic
Journal:
Proc. Amer. Math. Soc.
131
(2003),
745-754.
MSC (2000):
Primary 46E30, 26D10, 47B38, 47G10
Posted:
October 15, 2002
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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.
References:
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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, Zitná 25, 115~67 Praha 1, Czech Republic
Email:
opic@math.cas.cz
DOI:
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
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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