%0 Journal Article %T Weighted function spaces and Dunkl transform %A Chokri Abdelkefi %J Mathematics %D 2010 %I arXiv %X We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on Rd weighted Lp-estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L1 when this function belongs to a suitable Besov-Dunkl space. %U http://arxiv.org/abs/1005.5235v1