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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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