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We consider the continuous wavelet transform associated with the Weinstein operator. We introduce the notion of localization operators for . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of on sets of finite measure. In particular, Benedicks-type and Donoho-Stark’s uncertainty principles are given. Finally, we prove many versions of Heisenberg-type uncertainty principles for .

In this paper we consider the Dunkl operators Tj, j = 1, . . . , d, on R d and the harmonic analysis associated with these operators. We define a continuous Dunkl Gabor transform, involving the Dunkl translation operator, by proceeding as mentioned in [20] by C. Wojciech and G. Gigante. We prove a Plancherel formula, an L 2 k inversion formula and a weak uncertainty principle for it. Then, we show that the portion of the continuous Dunkl Gabor transform lying outside some set of finite measure cannot be arbitrarily too small. Similarly, using the basic theory for the Dunkl continuous wavelet transform introduced by K. Trimèche in [18], an analogous of this result for the Dunkl continuous wavelet transform is given. Finally, an analogous of Heisenberg's inequality for a continuous Dunkl Gabor transform (resp. Dunkl continuous wavelet transform) is proved. Mathematics Subject Classification (2000). 26D10, 43A32, 46C05, 46E22.