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Cherednik-Sobolev spaces and applications

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Abstract

In this paper we introduce and we study the Sobolev type spaces associated to Cherednik operators on \({\mathbb{R }}^{d}\). Next we define the generalized Besov and Triebel spaces and we study some of properties. As applications on these spaces we establish the Sobolev embedding, the hypoellipticity for the Cherednik operators. We give some properties including some estimates for the solution of the generalized wave equation and the generalized Schrödinger equation. Also, some applications are given for these spaces.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Taibah University, PO. Box 30002, Al Madinah, AL Munawarah, Saudi Arabia

    Hatem Mejjaoli

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  1. Hatem Mejjaoli
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Correspondence to Hatem Mejjaoli.

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Dedicated to Khalifa Trimèche.

Thanks to Professor K. Trimèche for his help and encouragement. Thanks is also due to the referee for his suggestions and comments.

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Mejjaoli, H. Cherednik-Sobolev spaces and applications. Afr. Mat. 26, 169–200 (2015). https://doi.org/10.1007/s13370-013-0191-1

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  • DOI: https://doi.org/10.1007/s13370-013-0191-1

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