Chokri Abdelkefi, Jean-Philippe Anker, Feriel Sassi, Mohamed Sifi, “Besov-Type Spaces on <nobr>$\mathbb R^d $</nobr> and Integrability for the Dunkl Transform”, SIGMA, 2009, Volume 5,019, 15 pp.

This article is cited in 16 papers

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

Chokri Abdelkefi^a, Jean-Philippe Anker^b, Feriel Sassi^a, Mohamed Sifi^c

^a Department of Mathematics, Preparatory Institute of Engineer Studies of Tunis, 1089 Monfleury Tunis, Tunisia
^b Department of Mathematics, University of Orleans \& CNRS, Federation Denis Poisson (FR 2964), Laboratoire MAPMO (UMR 6628), B. P. 6759, 45067 Orleans cedex 2, France
^c Department of Mathematics, Faculty of Sciences of Tunis, 1060 Tunis, Tunisia

Abstract: 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.

Keywords: Dunkl operators; Dunkl transform; Dunkl translations; Dunkl convolution; Besov–Dunkl spaces.

MSC: 42B10; 46E30; 44A35

Received: August 28, 2008; in final form February 5, 2009; Published online February 16, 2009

Language: English

DOI: 10.3842/SIGMA.2009.019