Mean convergence of Fourier–Dunkl series

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 A p classes of Muckenhoupt, which ensur...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 372; no. 2; pp. 470 - 485
Main Authors Ciaurri, Óscar, Pérez, Mario, Reyes, Juan Manuel, Varona, Juan Luis
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.2010
Elsevier
Subjects
Dunkl transform
Exact sciences and technology
Fourier analysis
Fourier–Dunkl series
Functions of a complex variable
Mathematical analysis
Mathematics
Mean convergence
Orthogonal system
Sciences and techniques of general use
Dunkl transform
Mean convergence
Orthogonal system
Fourier–Dunkl series
Necessary condition
Sufficient condition
Mathematical analysis
Series expansion
Fourier series
Fourier-Dunkl series
Convergence in mean
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Summary: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 A p classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.07.029