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

Full-text PDF

Abstract | References | Similar Articles | 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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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