On the theorems of Hardy and Miyachi for the Jacobi-Dunkl transform.

We generalize theorems of Hardy and Miyachi for the Fourier transform on real line to the Jacobi-Dunkl transform. More precisely in the first part of this paper we give another proof of the heart of Hardy's theorem (we mean αβ=1/4), which has been obtained recently by Chouchane, Mili, and Trimèche. In the second part, we get some analog of Miyachi's theorem for the Jacobi-Dunkl transform. [ABSTRACT FROM AUTHOR]