Besov-Type Spaces on $R^d$ and Integrability for the Dunkl Transform

Chokri Abdelkefi (1) , Jean-Philippe Anker (2) , Feriel Sassi (1) , Mohamed Sifi (1)

1 Analyse Mathématique et Applications
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper, we show the inclusion and the density of the Schwartz space in Besov-Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov-Dunkl space.

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Chokri Abdelkefi, Jean-Philippe Anker, Feriel Sassi, Mohamed Sifi. Besov-Type Spaces on $R^d$ and Integrability for the Dunkl Transform. Symmetry, Integrability and Geometry : Methods and Applications, 2009, 5, 019, 15 pp. ⟨10.3842/SIGMA.2009.019⟩. ⟨hal-00362680⟩