Mean convergence of Fourier-Dunkl series
- Ciaurri, Ó. 1
- Pérez, M. 2
- Reyes, J.M. 3
- Varona, J.L. 1
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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3
Universitat Pompeu Fabra
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ISSN: 0022-247X
Année de publication: 2010
Volumen: 372
Número: 2
Pages: 470-485
Type: Article
D'autres publications dans: Journal of Mathematical Analysis and Applications
Résumé
In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion associated to this system. We establish conditions on the weights, in terms of the Ap classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions. © 2010 Elsevier Inc.