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Mean convergence of Fourier-Dunkl series |
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| Authors: | Óscar Ciaurri Mario Pérez Juan Manuel Reyes |
| Institution: | a CIME and Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain b IUMA and Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain c Departament de Tecnologia, Universitat Pompeu Fabra, 08003 Barcelona, Spain |
| Abstract: | 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. |
| Keywords: | Dunkl transform Fourier-Dunkl series Orthogonal system Mean convergence |
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