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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
Posted:
October 15, 2002
MathSciNet review:
1937412
Full-text PDF Free Access
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Additional Information
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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 and  and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299. MR 34:3295
- [CKOP]
- A. Cianchi, R. Kerman, B. Opic and L. Pick, Sharp rearrangement inequality for the fractional maximal operator, Studia Math. 138 (2000), 277-284. MR 2001h:42029
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 , Pacific J. Math. 1 (1951), 411-429. MR 13:470c
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- E. T. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158. MR 91d:26026
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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
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
Article copyright:
© Copyright 2002 American Mathematical Society
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