Another proofs of the geometrical forms of Paley-Wiener theorems for the Dunkl transform and inversion formulas for the Dunkl interwining operator and for its dual

Paley type inequality on Hardy space in the Dunkl setting

We investigate $λ$-Hilbert transform, $λ$-Possion integral and conjugate $λ$-Poisson integral on the atomic Hardy space in the Dunkl setting and establish a new version of Paley type inequality which extends the results in \cite{F} and \cite{ZhongKai Li 3}.

Singular integral operators, $T1$ theorem, Littlewood-Paley theory and Hardy spaces in Dunkl Setting

The purpose of this paper is to introduce a new class of singular integral operators in the Dunkl setting involving both the Euclidean metric and the Dunkl metric. Then we provide the $T1$ theorem, the criterion for the boundedness on $L^2$ for these operators. Applying this singular integral operator theory, we establish the Littlewood-Paley theory and the Dunkl-Hardy spaces. As applications, the boundedness of singular integral operators, particularly, the Dunkl-Rieze transforms, on the Dunkl-Hardy spaces is given. The $L^2$ theory and the singular integral operator theory play crucial roles…

Some remarks on another proof of geometrical Paley-Wiener theorems for the Dunkl transform

We argue that another proof by Trimeche of the geometrical form of the Paley-Wiener theorems for the Dunkl transform is not correct.

线性规范Dunkl变换的实Paley-Wiener定理

Real Paley-Wiener theorems for the linear canonical Dunkl transform

本文研究了与线性规范Dunkl变换相关的Sobolev空间及算子性质，建立了实Paley-Wiener定理，刻画了变换支撑于多项式域的平方可积函数，并发展了Boas型Paley-Wiener定理。

关于Dunkl变换的几何Paley-Wiener定理一个证明的若干评注

Some remarks on a proof of geometrical Paley-Wiener theorems for the Dunkl transform

本文指出文献中Dunkl变换的几何Paley-Wiener定理的一个证明存在错误，并给出相应评注。

实直线上 Dunkl 变换的 Paley-Wiener 定理的初等证明

Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line

本文用初等方法证明了实直线上 Dunkl 变换对光滑函数与 L^2 函数的 Paley-Wiener 型定理，并给出 L^p 函数的 Bang 型恒等式，且对 Fourier 变换特例亦属新证明。