Mean convergence of Fourier-Dunkl series

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 $A_p$ classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions.

References in corpus (1)

• Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line

Cited by in corpus (1)

• Bilinear biorthogonal expansions and the Dunkl kernel on the real line