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FOURIER MULTIPLIERS FOR Lp ON CHÉBLI–TRIMÈCHE HYPERGROUPS

Published online by Cambridge University Press:  20 August 2001

WALTER R. BLOOM  and
ZENGFU XU
WALTER R. BLOOM
Affiliation:
Division of Science and Engineering, Murdoch University, Perth, WA 6150, Australia, bloom@murdoch.edu.au, zengfu@starwon.com.au
ZENGFU XU
Affiliation:
Division of Science and Engineering, Murdoch University, Perth, WA 6150, Australia, bloom@murdoch.edu.au, zengfu@starwon.com.au
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Abstract

In this paper we consider Fourier multipliers for $L^p$ $(p>1)$ on Chébli-Trimèche hypergroups and establish a version of Hörmander's multiplier theorem. As applications we give some results concerning the Riesz potentials and oscillating multipliers.

1991 Mathematics Subject Classification: 43A62, 43A15, 43A32.

Keywords

Fourier multipliers$L^p$ spaceshypergroup
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 80 , Issue 3 , May 2000 , pp. 643 - 664
Copyright
1999 London Mathematical Society

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