On the theorems of Hardy and Miyachi for the Jacobi–Dunkl transform

Abstract

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.

Keywords:

• Hardy's theorem
• Jacobi-Dunkl transform
• Heat kernel

Additional information

Notes on contributors

R. Daher

Email: [email protected]