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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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1869-6090
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On the boundedness of pseudo-differential operators associated with the Dunkl transform on the real line

Béchir Amri
  • Université de Tunis, Institut Préparatoire aux Etudes d'Ingénieurs de Tunis (IPEIT), Département de Mathématiques, 1089 Montfleury Tunis, Tunisia.
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/ Sami Mustapha / Mohamed Sifi
  • Université de Tunis El Manar, Faculté des Sciences de Tunis, Département de Mathématiques, 2092 Tunis, Tunisia.
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Published Online: 2010-05-31 | DOI: https://doi.org/10.1515/apam.2010.028

Abstract

In this paper we consider pseudo-differential operators associated with the Dunkl transform on the real line. We establish the Calderón–Vaillancourt theorem for such operators. We also obtain the Lp -boundedness for the Hörmander's class (0 ≤ δ < 1).

Keywords.: Dunkl transform; pseudo-differential operators; singular integrals

About the article

Received: 2009-03-28

Published Online: 2010-05-31

Published in Print: 2011-01-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2010.028.

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