Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 019, 15 pages      arXiv:0902.2765      https://doi.org/10.3842/SIGMA.2009.019
Contribution to the Special Issue on Dunkl Operators and Related Topics

Besov-Type Spaces on Rd and Integrability for the Dunkl Transform

Chokri Abdelkefi a, Jean-Philippe Anker b, Feriel Sassi a and 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

Received August 28, 2008, in final form February 05, 2009; Published online February 16, 2009

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.

Key words: Dunkl operators; Dunkl transform; Dunkl translations; Dunkl convolution; Besov-Dunkl spaces.

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