Mean convergence of Fourier-Dunkl series

Details Mean convergence of Fourier-Dunkl series Mean convergence of Fourier-Dunkl series

2010-10-09

arxiv.org/abs/1010.1848v1

J. Math. Math. Anal. Appl. 372 (2010), 470-485

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jmaa.2010.07.029

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.

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