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MIXED NORM ESTIMATES FOR POTENTIAL OPERATORS RELATED TO THE RADON TRANSFORM

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  01 April 2008

JAVIER DUOANDIKOETXEA  and
OSANE ORUETXEBARRIA
JAVIER DUOANDIKOETXEA*
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco-Euskal, Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain (email: javier.duoandikoetxea@ehu.es)
OSANE ORUETXEBARRIA
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco-Euskal, Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain (email: osane.oruetxebarria@ehu.es)
*
✉For correspondence; e-mail: javier.duoandikoetxea@ehu.es
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Abstract

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We define potential operators on hyperplanes and give sharp mixed norm inequalities for them. One of the operators coincides with the Radon transform for which mixed norm estimates are known but in reverse order. Those inequalities will be crucial in our proofs.

Keywords

potential operatorsRadon transformmixed norm estimates

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 181 - 191
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

Both authors supported in part by grant BFM2002-01550 of MCYT (Spain) and FEDER, and by European Project HPRN-CT-2001-00273-HARP.

References

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