Mean convergence of Fourier-Dunkl series
Functional Analysis
2012-11-06 v1 Classical Analysis and ODEs
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 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
Cite
@article{arxiv.1010.1848,
title = {Mean convergence of Fourier-Dunkl series},
author = {Ó. Ciaurri and M. Pérez and J. M. Reyes and J. L. Varona},
journal= {arXiv preprint arXiv:1010.1848},
year = {2012}
}