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387179

Some results on Dunkl analysis : A survey

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Last updated: 05 Jan 2025

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Abstract

In this article, we present a survey of some new results obtained in [2,8]. First, we give a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension. We also investigate the Lp fi Lq boundedness properties of the Riesz potentials Ija and the related fractional maximal function Mj,a associated to the Dunkl transform. Finally we prove the Lp-boundedness, (1 < p< 1) of the Riesz transforms in the Dunkl setting.

DOI

10.1016/j.joems.2011.09.001

Keywords

Dunkl operator, Paley–Wiener theorem, Generalized translations, Riesz potentials, Riesz transforms

Authors

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M.

Last Name

Sif

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Affiliation

Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia

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mohamed.sifi@fst.rnu.tn

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First Name

B.

Last Name

Amri

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Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia

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First Name

J-Ph

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Anker

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-

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Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia

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-

First Name

S.

Last Name

Hassani

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-

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Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia

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-

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-

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-

First Name

S.

Last Name

Mustapha

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-

Affiliation

Department of Mathematics, Faculty of Sciences of Tunis, 2092 Tunis, Tunisia

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Volume

19

Article Issue

1

Related Issue

50532

Issue Date

2011-06-01

Receive Date

2024-10-20

Publish Date

2011-06-01

Page Start

78

Page End

81

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 19_Issue 1_Pages 78-81.pdf

PDF . 363.3kB

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https://joems.journals.ekb.eg/article_387179.html

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https://joems.journals.ekb.eg/service?article_code=387179

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387,179

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

Some results on Dunkl analysis : A survey

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Article

Created At

21 Dec 2024