Hardy's type inequality for the over critical exponent associated with the Dunkl transform

\begin{abstract} For the Hardy space $H^p(\mathbb{R}^{d})$, $0<p\leq 1,$ we shall improve a Hardy's type inequality associated with Dunkl transform respect to the measures $d\mu_{k}$ homogeneous of degree $\gamma ,$ on the strip $(2\gamma+d)(2-p)\leq\sigma<2\gamma+d+p(N+1),$ where $N =[(2\gamma+d)(1/p-1)]$ is the greatest integer not exceeding $(2\gamma+d)(1/ p -1).$ \end{abstract}